Talk:Infraparticle

Article reduced

Considering concerns on the AFD and on my talk page, I've removed the OR portions of the article and kept the first paragraph only. It will be almost like re-building from scratch. --JForget 20:27, 31 December 2009 (UTC)

What happened to this article???

This used to be the single most informative Wikipedia article! I had no idea what an "infraparticle" was exactly until I read this article, which explained the idea so clearly. It was nominated for deletion, and now it has been completely decimated. I will first restore the relevant text to the talk page for safekeeping.

See the concerns at this [[1]] to see why the article was stubbified, a lot of the article was unreadable and OR. --JForget 22:48, 19 February 2010 (UTC)

I saw that discussion. Please use the term "OR" correctly --- OR means unsourcable material, not unsourced material. This material is well known, and appears in the literature. It reads funny because it is very good discussion from many years ago, when material was not subject to this kind of detailed Wikipedia-rules-based scrutiny.

This material is so not OR, that it is frightening to me that you would delete it. A simple review of the literature on infraparticles would have spared the trouble of these discussions. Anyway, I hope that similar articles of comparably high quality are not subject to the same treatment.Likebox (talk) 22:51, 19 February 2010 (UTC)

Old (excellent) Article content

In electrodynamics and quantum electrodynamics, in addition to the global U(1) symmetry related to the electric charge, there are also position dependent gauge transformations. Noether's theorem states that for every infinitesimal symmetry transformation that is local (local in the sense that the transformed value of a field at a given point only depends on the field configuration in an arbitrarily small neighborhood of that point), there is a corresponding conserved charge called the Noether charge, which is the space integral of a Noether density (assuming the integral converges and there is a Noether current satisfying the continuity equation).

If this is applied to the global U(1) symmetry, the result

$Q=\int d^{3}x\rho ({\vec {x}})$ (over all of space)

is the conserved charge where ρ is the charge density. As long as the surface integral

$\oint _{S^{2}}{\vec {J}}\cdot d{\vec {S}}$

at the boundary at spatial infinity is zero, which is satisfied if the current density J falls off sufficiently fast, the quantity Q is conserved. This is nothing other than the familiar electric charge.

But what if there is a position dependent (but not time dependent) infinitesimal gauge transformation $\delta \psi ({\vec {x}})=iq\alpha ({\vec {x}})\psi ({\vec {x}})$ where α is some function of position?

The Noether charge is now

$\int d^{3}x\left[\alpha ({\vec {x}})\rho ({\vec {x}})+\epsilon _{0}{\vec {E}}({\vec {x}})\cdot \nabla \alpha ({\vec {x}})\right]$

where ${\vec {E}}$ is the electric field.

Using integration by parts,

$\oint _{S^{2}}\alpha {\vec {E}}\cdot d{\vec {S}}+\int d^{3}x\alpha \left[\rho -\epsilon _{0}\nabla \cdot {\vec {E}}\right]$

This assumes that the state in question approaches the vacuum asymptotically at spatial infinity. The first integral is the surface integral at spatial infinity and the second integral is zero by the Gauss law. Also assume that α(r,θ,φ) approaches α(θ,φ) as r approaches infinity (in polar coordinates). Then, the Noether charge only depends upon the value of α at spatial infinity but not upon the value of α at finite values. This is consistent with the idea that symmetry transformations not affecting the boundaries are gauge symmetries whereas those that do are global symmetries. If α(θ,φ)=1 all over the S², we get the electric charge. But for other functions, we also get conserved charges (which are not so well known).

This conclusion holds both in classical electrodynamics as well as in quantum electrodynamics. If α is taken as the spherical harmonics, conserved scalar charges (the electric charge) are seen as well as conserved vector charges and conserved tensor charges. This is not a violation of the Coleman-Mandula theorem as there is no mass gap. In particular, for each direction (a fixed θ and φ), the quantity

$\lim _{r\rightarrow \infty }\epsilon _{0}r^{2}E_{r}(r,\theta ,\phi )$

is a c-number and a conserved quantity. Using the result that states with different charges exist in different superselection sectors, the conclusion that states with the same electric charge but different values for the directional charges lie in different superselection sectors.

Even though this result is expressed in terms of a particular spherical coordinates, in particular with a given origin, it is easy to see that translations changing the origin do not affect spatial infinity.

The directional charges are different for an electron that has always been at rest and an electron that has always been moving at a certain nonzero velocity (because of the Lorentz transformations). The conclusion is that both electrons lie in different superselection sectors no matter how tiny the velocity is. At first sight, this might appear to be in contradiction with Wigner's classification, which implies that the whole one-particle Hilbert space lies in a single superselection sector, but it is not because m is really the greatest lower bound of a continuous mass spectrum and eigenstates of m only exist in a rigged Hilbert space. The electron, and other particles like it is called an infraparticle.

The existence of the directional charges is related to soft photons. The directional charge at $t=-\infty$ and $t=\infty$ are the same if we take the limit as r goes to infinity first and only then take the limit as t approaches infinity. If we interchange the limits, the directional charges change. This is related to the expanding electromagnetic waves spreading outwards at the speed of light (the soft photons).

More generally, there might exist a similar situation in other quantum field theories besides QED. The name "infraparticle" still applies in those cases.

Explanation

This article explained two things which are both related: one of which is the Noether procedure for gauge symmetries. You expect that a gauge symmetry will produce an infinite number of conservation laws, one for each point in space, because there are an infinite number of symmetries, one for each point in space. Everybody knows that this doesn't work, because the Noether procedure gives a charge which is a perfect divergence.

But what this article shows is that this procedure actually does work, because the gauge transformation at infinity gives rise to a conserved current for each gauge transformation at infinity. This then allows you to define different superselection sectors, which are defined by the electric and magnetic fields at infinity. This is encyclopedic content of the highest quality, written by one of the best physics contributors ever (User:Phys, who left the site very early on). It is important not to delete what you don't understand--- just leave it alone. If it really is bad content, someone who does understand it will delete it. This used to be, hands down, the best article in the encyclopdia.Likebox (talk) 06:32, 18 February 2010 (UTC)

AfD

Everything in this article can be easily verified from first principles by any competent physicist. It is not OR, since the concept of infraparticle is at least 40 years old. I request that if you don't understand it, don't nominate it for deletion. This material is hard to find, occurs only sporadically in the literature, and is the chief source of value of the encyclopedia for working physicists. Without articles such as this, Wikipedia would not be useful.Likebox (talk) 06:58, 18 February 2010 (UTC)

I agree that the maths content should not be deleted, unless it is demonstrably false. Instead stick it all in a maths section or something. We should retain links to concepts such as infrared divergence. Even so, the text needs drastic improvement, and I couldn't tell what the concept was about. For example:

1. By "charged", do we mean "electrically charged"
2. "delta function of states at infinity"?? What states? Photon states? Or the particle's states?
3. Are all "charged" particles infraparticles?
4. Same effect with gravitons?

--Michael C. Price ^talk 08:49, 18 February 2010 (UTC)

1. yes
2. they're mixed up--- the infraparticle is an amalgam of particle+field
3. yes (electrically charged)
4. yes (almost certainly--- although the analysis is more difficult and I haven't thought how to do it)

The issue here is that an article was butchered while no-one was looking, and it was only by an accident that I noticed the change. The reason is that the original author left Wikipedia, possibly because he/she was annoyed at the too-low level of science discussions.Likebox (talk) 22:35, 18 February 2010 (UTC)

I noticed now you put the word "charged" in quotes, so I suppose you are asking if objects in other field theories which can be thought of as charged are infraparticles. Some surprises--- scalars interacting with scalars in 4d are not infraparticles (I can't verify this, I read it somewhere) so Nucleons interacting with massless pions are ok. The infrared divergences in gauge theory really give rise to new conservation laws at infinity, and this is the best way to express the effect.

Higgsed gauge fields don't show up at infinity, and neither do confined fields. So really, gravity is the only option. That and certain weird theories which are believed to be conformal in the infrared, like QCD with 16 quark flavors, or certain supersymmetric models.Likebox (talk) 23:33, 18 February 2010 (UTC)

(deindent) The reason this article is hard to read is because it assumes that the reader is intuitively familiar with a more advanced concept from quantum field theory: the density of states of interacting quantum fields. This is a delta function when you have a particle with definite mass M, it is a superposition of delta-functions (the scattering amplitude gets a cut) for two interacting particles of masses M and m, and the cut starts at m+M. and in this case, the cut coincides with the pole, because the photon is massless. This can do nothing unusual, or it can smear out the delta-function in the density of states to a power-divergence at M. If the smearing happens, you have an infraparticle (an unparticle is also a particle with a powerlaw density of states, which is why the author of the current reference provided by Headbomb tries to identify infraparticle and unparticle physics--- I am not sure if this identification is valid).Likebox (talk) 00:37, 19 February 2010 (UTC)

Source

The original source for this seems to be this article: D. Buchholz, Phys. Lett. B 174 (1986) 331. There, the discussion of Gauss's law is extended for the infraparticle case, and this parallels the discussion here. I have not had time to review this source in any detail (it was just linked from the one reference found here), and there might be an earlier one.Likebox (talk) 08:23, 18 February 2010 (UTC)

Proposed expansion

proposed expansion

Infraparticles are charged particles permanently surrounded by an electric field. They have strange quantum mechanical properties, because the classical field can be thought of as an infinite cloud of soft photons. Charged particles radiate an infinite number of soft photons whenver they change directions, these are the cause of the infrared divergences of quantum electrodynamics. The form of the electric field at infinity, which is determined by the velocity of a point charge, defines superselection sectors for the particle's Hilbert space. This is unlike the usual Fock space description, where the Hilbert space includes particle states with different velocities.

Because of their infraparticle properties, charged particles do not have a sharp delta-function density of states like an ordinary particle, but are accompanied by a soft tail of density of states which consist of all the low energy excitation of the electromagnetic field.

Noether's theorem for gauge transformations

In electrodynamics and quantum electrodynamics, in addition to the global U(1) symmetry related to the electric charge, there are also position dependent gauge transformations. Noether's theorem states that for every infinitesimal symmetry transformation that is local (local in the sense that the transformed value of a field at a given point only depends on the field configuration in an arbitrarily small neighborhood of that point), there is a corresponding conserved charge called the Noether charge, which is the space integral of a Noether density (assuming the integral converges and there is a Noether current satisfying the continuity equation).

If this is applied to the global U(1) symmetry, the result

$Q=\int d^{3}x\rho ({\vec {x}})$ (over all of space)

is the conserved charge where ρ is the charge density. As long as the surface integral

$\oint _{S^{2}}{\vec {J}}\cdot d{\vec {S}}$

at the boundary at spatial infinity is zero, which is satisfied if the current density J falls off sufficiently fast, the quantity Q is conserved. This is nothing other than the familiar electric charge.

But what if there is a position dependent (but not time dependent) infinitesimal gauge transformation $\delta \psi ({\vec {x}})=iq\alpha ({\vec {x}})\psi ({\vec {x}})$ where α is some function of position?

The Noether charge is now

$\int d^{3}x\left[\alpha ({\vec {x}})\rho ({\vec {x}})+\epsilon _{0}{\vec {E}}({\vec {x}})\cdot \nabla \alpha ({\vec {x}})\right]$

where ${\vec {E}}$ is the electric field.

Using integration by parts,

$\oint _{S^{2}}\alpha {\vec {E}}\cdot d{\vec {S}}+\int d^{3}x\alpha \left[\rho -\epsilon _{0}\nabla \cdot {\vec {E}}\right]$

This assumes that the state in question approaches the vacuum asymptotically at spatial infinity. The first integral is the surface integral at spatial infinity and the second integral is zero by the Gauss law. Also assume that α(r,θ,φ) approaches α(θ,φ) as r approaches infinity (in polar coordinates). Then, the Noether charge only depends upon the value of α at spatial infinity but not upon the value of α at finite values. This is consistent with the idea that symmetry transformations not affecting the boundaries are gauge symmetries whereas those that do are global symmetries. If α(θ,φ)=1 all over the S², we get the electric charge. But for other functions, we also get conserved charges (which are not so well known).

This conclusion holds both in classical electrodynamics as well as in quantum electrodynamics. If α is taken as the spherical harmonics, conserved scalar charges (the electric charge) are seen as well as conserved vector charges and conserved tensor charges. This is not a violation of the Coleman-Mandula theorem as there is no mass gap. In particular, for each direction (a fixed θ and φ), the quantity

$\lim _{r\rightarrow \infty }\epsilon _{0}r^{2}E_{r}(r,\theta ,\phi )$

is a c-number and a conserved quantity. Using the result that states with different charges exist in different superselection sectors, the conclusion that states with the same electric charge but different values for the directional charges lie in different superselection sectors.

Even though this result is expressed in terms of a particular spherical coordinates, in particular with a given origin, it is easy to see that translations changing the origin do not affect spatial infinity.

Implication for particle behavior

The directional charges are different for an electron that has always been at rest and an electron that has always been moving at a certain nonzero velocity (because of the Lorentz transformations). The conclusion is that both electrons lie in different superselection sectors no matter how tiny the velocity is. At first sight, this might appear to be in contradiction with Wigner's classification, which implies that the whole one-particle Hilbert space lies in a single superselection sector, but it is not because m is really the greatest lower bound of a continuous mass spectrum and eigenstates of m only exist in a rigged Hilbert space. The electron, and other particles like it is called an infraparticle.

The existence of the directional charges is related to soft photons. The directional charge at $t=-\infty$ and $t=\infty$ are the same if we take the limit as r goes to infinity first and only then take the limit as t approaches infinity. If we interchange the limits, the directional charges change. This is related to the expanding electromagnetic waves spreading outwards at the speed of light (the soft photons).

More generally, there might exist a similar situation in other quantum field theories besides QED. The name "infraparticle" still applies in those cases.

References

I think this is fine, now that the original source is present. It is important to emphasize that there are dozens if not hundreds of other sources for infraparticle behavior, starting in the 1960s. I don't know all this literature.Likebox (talk) 03:03, 19 February 2010 (UTC)

If there are dozens if not hundreds of sources for this, it should be easy to find a few that supports this material. Currently, most of the text is not supported by any references, and thus is removable per WP:Original Synthesis. I'm not objected to an expansion of the article, but it has to be sourced and verifiable. Basing most of this article on a preprint is also worrysome. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 17:59, 19 February 2010 (UTC)

I found a few, and I will give them here as soon as I review them (google for Buchholz). But I am curious--- what part of this discussion are you objecting to? I don't see anything the least bit objectionable. If you delete this, you are destroying the best article on Wikipedia, and its best reason for existence.Likebox (talk) 18:06, 19 February 2010 (UTC)

Everything, as this is unsourced, and this doesn't not match anything I come across when search google. From WP:V:

This policy requires that a reliable source in the form of an inline citation be supplied for any material that is challenged or likely to be challenged, and for all quotations, or the material may be removed. This is strictly applied to all material in the mainspace—articles, lists, and sections of articles—without exception [...]

The material is not only likely to be challenged, it is challenged. Either source it, or live with the stub version. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 18:40, 19 February 2010 (UTC)

(deindent) What are you challenging exactly, so I can know what you want sourced? What statements don't you agree with?Likebox (talk) 18:55, 19 February 2010 (UTC)

These statements. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 19:15, 19 February 2010 (UTC)

That's a joke! This is a long article, and I really have no idea what you want sourced. Most of the discussion is of old Noether's theorem for electric charge, which appears in all textbooks. The specific application of Noether's theorem for infraparticles appear in Buchholz. Putting them side by side does not constitute any synthesis.

Perhaps you are objecting to the mention of "rigged hilbert space?" I can source that too. Perhaps you are objecting to the "power law tail of the density of states?" I can source that as well. Please explain in detail what your objections are, so that they can be met.Likebox (talk) 19:36, 19 February 2010 (UTC)

I still have problems with the language. I can't tell to what extent the infraparticle is just the infrared divergence repackaged in fancy lingo.

The statement "the classical field can be thought of as an infinite cloud of soft photons." is surely not correct: a classical electric field is not composed of photons, since the photon is a quantum concept.

The "superselection sector" needs a lot of explanation. I have no idea at all what it means.

--Michael C. Price ^talk 23:47, 19 February 2010 (UTC)

There is no consensus here to include material from this proposed expansion until it is properly sourced. Please comply with WP:V. Thank you.—Finell 00:02, 20 February 2010 (UTC)

I'm not sure there is a consensus to delete it either. I'd rather see the above language and conceptual issues addressed first before we start sourcing it all. --Michael C. Price ^talk 00:09, 20 February 2010 (UTC)

That is the reverse of Wikipedia's process. First you do the research (i.e., you find relevant reliable sources), then you add material to the article based on what the sources say. I have no objection to setting up a talk subpage here to work on a draft of the expanded article. Even in doing that, it would be more efficient (and have a better chance of winding up with a correct article) to start with the sources and summarize them, rather than writing the article without sources, then look for sources to support what Wikipedians write. However, there is no policy against writing an unsourced draft outside article space, if that is how you prefer to go about it.

There is a policy against having unsourced content in articles when the content is challenged; this unsourced content, as Headbomb noted, is challenged. The edit comment for Michael's last revert says, "Actually a lot of that is sourced ...." At present, there are only 2 statements in the lead supported by cited sources. If sources for the re-added material is at hand, cite them. If not, remove them until you have sources. Let's please follow policy in this article itself. Thank you.—Finell 00:32, 20 February 2010 (UTC)

It's true that the sourced statements I was thinking of were the ones in the lead. However they were reverted as part of the block revert, so I feel my complaint was at least partially justified.

I agree that a draft article might be the best way forward. --Michael C. Price ^talk 01:10, 20 February 2010 (UTC)

I'm against following policies when it has ridiculous consequences. Except for Michaels comments, the content has not been challenged based on a factual discussion at all. On Wikipedia, we don't only procedurally challenge a text based on missing citations (with the exception of non-scientific topics). Acting in that way would be a disaster as that gives quack editors the right to Wikilayer when they have been proved wrong based on the facts. Take e.g. the article Heim theory which is a pseudoscientific quack theory. I actually voted for keeping that article during a VFD, on the grounds that Wikipedia can have articles on any subject. But I was asked by my fellow physicst editors at the time (who voted to delete that article), that I should now take some time to make that article more acceptable. SCZenz and I have editited in some qualifications in that article giving a reasonable physics perspective which question the validity of Heim theory. However, all this is 100% OR (in the sense that it is not supported by any citations); no physicist will waste its time debunking an obvious quack theory. This has been done with the agreement of the few editors who support Heim theory. Count Iblis (talk) 01:28, 20 February 2010 (UTC)

(deindent) This debate is ridiculous--- I challenge Finnell to find one example of an article which was originally written from sources (there are a handful, none in science). The correct way to write a Wikipedia article is just to be bold and write it, wait for people to come in and challenge things, and then source the statements and counterstatements as all the points of view come into focus. This is how all articles have been written in the past, and how all good articles will be written in the future.

In particular, stuff that is unchallenged does not need to be sourced. I don't know what statements people are challenging in this article, and on what basis they are challenging them, so it is hard to know what to source. Are you challenging the Noether theorem stuff? That's easy to source. The Noether theorem in the gauge case? That's also easy. The superselection stuff? What? It's completely unclear. The whole thing was deleted because somebody thought that it "smells like OR". I got news for you: all mathematical articles "smell like OR" to people who don't understand the mathematics, which is why we need a good policy regarding mathematical content. Otherwise every high caliber discussion (like this one) will end up deleted by the first administratively minded person who doesn't understand it.

This article was written many years ago by a top-notch physicist, who left the project, probably because he or she had better things to do. Deleting this article is exactly like deleting an article written by Albert Einstein. There is nothing in this article which is original, and there is nothing which is controversial.Likebox (talk) 02:13, 20 February 2010 (UTC)

About sources--- I found the Buchholz source, and an anonymous IP independently suggested the exact same source. Everything in here can be found in that '86 paper.Likebox (talk) 02:50, 20 February 2010 (UTC)

Likebox appealed to Jimbo at User talk:Jimbo Wales#An old quote about the necessity of sources in articles of this kind. Here is Jimbo's reply:

I think you are asking two questions in one. Should mathematical/technical content, for example in physics, be sourced? Absolutely, it must be sourced, and this is one of the most important areas where sourcing has to be taken seriously, because we are not the right place for original research. (And as I'm sure you are aware, physics is one area where crackpots on the Internet are numerous.) Should editors without a technical background tread lightly in areas where they don't have much expertise? Yes, of course. But that doesn't mean that these editors can't insist quite firmly on quality, and quality means (among other things) making specialist material comprehensible to thoughtful nonspecialists (this is an encyclopedia, after all, not a journal of physics). It can be challenging yes, but it should be clear and should serve as a beacon of light to the reader.--Jimbo Wales (talk) 15:09, 20 February 2010 (UTC)

—Finell 19:50, 20 February 2010 (UTC)

First, the question wasn't over whether articles should be sourced: of course they should be sourced. The question is whether the sources should be read and understood and the mathematics verified patiently by editors. I wasn't "appealing to Jimbo", because he has no special authority on this matter. I asked him whether he thought that the use of his words above were appropriate.Likebox (talk) 21:11, 20 February 2010 (UTC)

And you got your answer. It isn't the one you wanted.—Finell 23:12, 20 February 2010 (UTC)

Wales is not a scientific editor, and perhaps he misunderstood. Perhaps he said something stupid. Whatever. If people keep deleting material like this, 1. I'm outta here, 2. you won't be seing any serious science on this encyclopedia.Likebox (talk) 00:00, 21 February 2010 (UTC)

Note that by bringing up Likebox'posting on Jimbo's userspace, Finell had something to argue about while being able to avoid addressing the content of the article. Count Iblis (talk) 00:27, 21 February 2010 (UTC)

Michael Price's questions

Michael Price made an attempt to grapple with the article content

I still have problems with the language. I can't tell to what extent the infraparticle is just the infrared divergence repackaged in fancy lingo.

The statement "the classical field can be thought of as an infinite cloud of soft photons." is surely not correct: a classical electric field is not composed of photons, since the photon is a quantum concept.

The "superselection sector" needs a lot of explanation. I have no idea at all what it means.

--Michael C. Price ^talk 23:47, 19 February 2010 (UTC)

In fact, the infraparticle is exactly the infrared divergence, which is the reason for the name. The infrared divergence is perturbative, it exists in a theory defined with a charged particle Fock space and a photon Fock space which are separate. But the infrared divergences tell you that the two Fock spaces are not separate and mix up. The infraparticle is what you get in the nonperturbative theory when you deal with the infrared divergences.

An infraparticle consists of a charged particle plus its cloud of soft photons. Of course, this is the quantum case, in the classical case, the analog of the infraparticle is a particle with its field. The point is that the field is long ranged enough so that if the particle is moving in different directions, an infinite number of soft photons at infinity are arranged in a different way.

A superselection sector is (loosely speaking) a state of a quantum theory which is like the vacuum, but has infinitely many particles in it, compared to the ordinary vacuum. For example, in the mexican hat potential, each different direction of the mexican hat field is a different superselection sector (a different vacuum). But superselection sectors are not just properties of the vacuum--- they happen whenever you can't get from state A to state B by any local fluctuation. The simplest example is the Ising model below the phase transition point. Another example is the vacuum space of D-branes. Another example is this infraparticle business--- each state with a definite momentum is in a different superselection sector. In order to knock the particle into another velocity you need to scatter it off something else, and then you get infinitely many soft photons out, so the field at infinity takes forever to change.Likebox (talk) 02:13, 20 February 2010 (UTC)

The best example of a superselection sector is in a 3+1 d scalar model with two vacua. If you have a domain wall in the theory, each position of an infinite 2+1 d domain wall is a superselection sector. This example is good because it isn't a vacuum, it is well known, and it has an obvious classical limit.Likebox (talk) 02:52, 20 February 2010 (UTC)

Don't tell us here - add it to the article, or at links to the article!

And please don't leave so many lazy redlinks around. I've set up two redirects for redlinks that were in the lead. --Michael C. Price ^talk 04:21, 20 February 2010 (UTC)

Thanks for fixing that, I was in a hurry. I didn't feel comfortable adding to the article, because I thought of it as the "perfect article", but your additions made it clearer.Likebox (talk) 06:29, 20 February 2010 (UTC)

Oh, please! Your so-called "perfect article" is rated stub-class. It isn't even a GA. If you think it is a "perfect article", take it to FaR. Don't propose the current version; propose your version. Otherwise, can the ridiculous hyperbole.—Finell 19:24, 20 February 2010 (UTC)

The science articles that are GA are not useful for working scientists. Although they are valuable for students, they do not convey actual hard-to-find expert knowledge.

This article, along with BKL singularity, conveys actual expert knowledge in a way that makes it widely accessible. This material is obscure enough that, without this article, only a thousand or so experts are familiar with this business. With this article, all working physicists can become familiar with it.

This is the central mission of Wikipedia--- disseminating specialist knowledge broadly. Let me list a few articles which should be written like this one: QCD sum rules, Penguin diagram, Kraichnan model, N/D equations, Pomeron. These articles are all nonexistent or devoid of any mathematical content. Why is that? Why aren't a bunch of experts eagerly advertising these fields by writing technical content?

The reason is that these experts are scared that they will have to argue with people who don't understand the material over nonsense like this. I don't think I could convince you that ths article is OK, even with a hundred sources, because you wouldn't read them with understanding. This is the most important requirement--- understand what you edit, especially what you delete.Likebox (talk) 21:04, 20 February 2010 (UTC)

I'm getting tired of your repeated accusations of idiocy and of us lacking the capabilities to understand anything beyond simple algebra. WP:V is a policy, not some trivial thing you can disregard because you find it a hassle to follow. And so is WP:NPA, which I suggest you start to follow, now. Wikipedia is not a science vulgarization blog, it's an encyclopedia, and things need to be sourced, and not rely on the "prestige" of the author of the material. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 21:13, 20 February 2010 (UTC)

I have never accused anyone of anything, nor have I made personal attacks. All I said is that I gave you a source, and nothing changes. You still say the material is OR, even after I showed you the exact article that contains the arguments here (Buchholz '86).

That isn't idiocy--- it's lazy editing. I have not gotten an answer about whether you think the new source is a good source, or what exactly is wrong with the page given the new sourcing. It took me a bit of work to understand and check this page (I did it several years ago), I don't think that you have put in this work yet. Please do.Likebox (talk) 21:21, 20 February 2010 (UTC)

Hold Your Horses on Deletion!

All the sections here can be easily sourced--- give the editors time to review the literature and find the appropriate citations. This is well known material, and there is no reason to hastily delete it. Deleting long discussions without consensus can be construed as vandalism.Likebox (talk) 22:20, 20 February 2010 (UTC)

Hold Your Horses on Adding Unsourced Content! When you source the content, you can restore the content. See WP:BURDEN.—Finell 23:10, 20 February 2010 (UTC)

Some unclear tags:

1. "is a c-number and a conserved quantity" was tagged, but it wasn't clear what the editor wanted.
2. "translations changing the origin do not affect spatial infinity" It was also unclear to me what was being challenged in this obvious statement. It is saying that if you take Er^2 over a ball centered at the origin, it doesn't matter what origin you take if r is large enough. I don't know what is unclear about this.
3. "The conclusion holds in classical electrodynamics as well as quantum electrodynamics"--- I also don't know what to say here: Noether's theorem is classical+quantum. I don't know what the editor is challenging exactly.

I will source the particle stuff from Buchholz latest book.Likebox (talk) 23:33, 20 February 2010 (UTC)

I sourced it from a 1982 article instead.Likebox (talk) 23:51, 20 February 2010 (UTC)

Lead tags

The (well known) statement about soft photon measurement threshold is copied verbatim from infrared divergence. If you have issues with this statement, please take your concerns there, because this is a topic too elemetary to deal with for this article.Likebox (talk) 23:47, 20 February 2010 (UTC)

Noether charge for gauge transformations

The Noether procedure for global gauge transformation produces the electric current and charge. The Noether procedure for local gauge transformations produces nothing new when the gauge transformation is constant at infinity. This is common knowledge, and contained in every field theory text. I don't know what you want for a source, because you just put the tag without explaining the point of contention. Please make the disputed point clear.Likebox (talk) 03:28, 21 February 2010 (UTC)

If it's contained in every text, then it should be an easy feat to find one. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 04:49, 21 February 2010 (UTC)

It's as annoying as sourcing "F=ma". When you know something so intuitively, you don't remember where you first read it. This type of citation request is absurd, but here you go:

For starters, there's the comment at the end of this link which states that the gauge symmetry gives electric charge (but doesn't do the detailed derivations). The details are in Karatas and Kowalski, "Noether's Theorem for Local Gauge Transformations", which derives the charge and current. But these sources are annoying. There's a good paper by Hawking which does a quick review of Noether's theorem by the quick gauging method, which citation I can't remember (I know the method), and that's the best reference.

It is ridiculous to have to source such a well-known thing. It's like asking someone to source commutativity of integer addition on an algebra page.Likebox (talk) 05:04, 21 February 2010 (UTC)

I don't care if they're annoying, they are necessary. Wikipedia readers does not consist of solely of particle physics experts, who are familiar with the Noether theorem and the required maths to "know for themselves" that what is written here isn't a load of crap. It's a well known fact that Murray Gell-Man and George Zweig proposed the quark model in 1964. That doesn't mean it doesn't have to be sourced. This isn't high-school physics, you can't assume that the reader has gone through even a Master's degree in particle physics, let alone a PhD (which wouldn't even guarantee that they've encountered the Noether theorem in more than a passing mention). Headbomb {^ταλκ_{κοντριβς} – WP Physics} 14:16, 21 February 2010 (UTC)

The point is--- such readers have no business deleting this material. It assumes that you are already familiar with Noether's theorem, with quantum field theory, etc. Before deleting, find out if the material is accurate. When you are dealing with expert knowledge, as Jimmy Wales' said, tread lightly. In particular, you should save deleted mathematical material to the talk page, as I did, so people don't have to go digging through the history for the TeX.Likebox (talk) 21:52, 21 February 2010 (UTC)

(deindent) To Headbomb: asking for sources where a detailed argument can be given for material at such high level is what kills the growth of mathematical articles. It would be much better if you were to request a detailed mathematical derivation of the result, which can be added to the relevant article. Accurate mathematical content is never going to get written by reviewing sources and copying the contents. Never, under any circumstances, period.Likebox (talk) 22:01, 21 February 2010 (UTC)

Likebox, it's a good idea not to talk down to other editors even when you have evidence that they know less than you. I would gladly help source annoying points. The divergence theorem actually provides the point you are trying to make and it was first proposed as an idea, arguably, by Gauss. We could cite Gauss directly, in fact. ScienceApologist (talk) 10:19, 22 February 2010 (UTC)

Current density

Infraparticle#Noether's theorem for gauge transformations contains the follwing: "... at the boundary at spatial infinity is zero, which is satisfied if the current density J falls off sufficiently fast ..." The link is to electromagnetic current density. Should the link be changed to probability current? Or to Probability density function?—Finell 13:36, 21 February 2010 (UTC)

For a charged particle, they're proportional to each other, so it may not matter. --Michael C. Price ^talk 15:58, 21 February 2010 (UTC)

Michael Price is talking about the relation between the charged particle current and probability density, but in this case, the author is talking about current and field densities, but whatever, it is correct as written. Anyway, all the sourcing (except for Buchholz) is to stuff that is absurdly well known and must be intuitively familiar before this article makes any sense.Likebox (talk) 21:55, 21 February 2010 (UTC)

The discussion here is phrased carefully so that it applies to the classical and quantum case, and to an arbitrary source of electric current in the quantum case. It is not proper to replace "current density" with "probability current density", since they are only proportional in the nonrelativistic limit for a single particle with charge. This discussion is for all possible sources. This question is not at all relevant to infraparticle, but is part of the assumed background that every reader should know, so I please ask: put in the effort to learn the background and learn the subject before making changes.Likebox (talk) 22:12, 21 February 2010 (UTC)

Headbomb made that change. Perhaps you need to clarify the text.—Finell 00:15, 22 February 2010 (UTC)

Revert, per admission of deceptive sourcing by Likebox

See [2]. I've reverted to the stub version in the meantime, so we make sure to not mislead readers. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 00:19, 22 February 2010 (UTC)

This comment is saying that the editors here did not bring up any of the substantive issues with infraparticles, and instead asked for sourcing of the most obvious, simple to source, trivialities which have nothing to do with the subject. Providing such sourcing is smoke and mirrors--- it distracts from the real issues with infraparticles. The sources I provided were accurate for the material that was challenged, it's just that the challenges were not very astute.Likebox (talk) 16:34, 22 February 2010 (UTC)

We've also only had about two days to review the article, during the week-end, while most of us are not at university where we can't check the given sources. If you want more serious challenges, give it time, and they will come. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 16:51, 22 February 2010 (UTC)

Until you produce those challenges, you should leave the article alone.Likebox (talk) 18:47, 22 February 2010 (UTC)

Draft version

That version can be found here.

Here, we can work on this in the meantime. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 00:26, 22 February 2010 (UTC)

Do you think that a talk subpage, rather than this hidden section, would be a more convenient platform for editing a draft?—Finell 05:59, 22 February 2010 (UTC)

No idea. I don't care either way, as long as we get to review the sources in details and make sure they support what they are claimed to support. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 06:16, 22 February 2010 (UTC)

You two should be ashamed of yourselves. --Michael C. Price ^talk 06:11, 22 February 2010 (UTC)

Yes, striving for quality articles with quality referencing, factual accuracy and no original synthesis is abhorrent, we are aware. In the meantime, if you're so disgusted by us, I suggest you disengage and come back after you more concerned with the quality of this article than in discussing the personal character of Finell and I. The world won't end if they stumble upon a stub version of this article for one more week or so, and it's a much better situation than having them read a deceptively sourced article, potentially containing falsehoods and original synthesis. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 06:25, 22 February 2010 (UTC)

Article protected

The article has been full protected as a result of User:Count Iblis's repeated re-addition of the unsourced, disputed content.

Count: If adding the sources is "trivial", as you edit content says, why don't you just do it, instead of scolding and pontificating to everyone else. This was your modus operandi at Speed of light, where

• You said that the article's editors were irresponsible for having inaccurate information in the article—but you didn't correct.
• You told us all how we could easily resolve the year long dispute with Brews ohare, and the dispute with Tombe—but you didn't employ your methods to resolve these serious disputes.

Your preaching without helping is getting really old.—Finell 06:10, 22 February 2010 (UTC)

{{Editprotected}} Could an administrator please add the full protected icon to the article? Thanks.—Finell 06:10, 22 February 2010 (UTC)

 Done — Martin (MSGJ · talk) 08:06, 22 February 2010 (UTC)

As Scienceapologists points out below, first we need to know what needs to be sourced. But then I also think we're putting the horse behind the cart here. We need to first agree on what the introductory paragraph should explain. My opinion is that you cannot then just say that we are a priori bound to what some article on infraparticles is writing about. I think this is the real source of the dispute. If you add a good introductory paragraph then you may need to go beyond what the source ion the subject itself is itself explaining, thereby making sourcing to satisfy the die hard wiki-fundamentalists more difficult. If you want to make sourcing very easy, then the article will probably remain in stub form. Count Iblis (talk) 13:26, 22 February 2010 (UTC)

Count: I would very much like to see a good introduction to this article, especially one that is helpful to the general reader (to the extent that is possible). I have never taken the position that fairly summarizing what sources say, or translating them into non-technical (or less technical) language, is WP:OR. I don't even mind connecting the dots between sources, provided the connections are non-controversial. To me, WP:SYNTH is where a Wikipedian reaches a new conclusion, using conclusions from multiple sources as premises, but where no reliable source draws the same conclusion. I also agree with your statement that a good introduction would lay a foundation for the concepts that a journal article on infraparticles would expect the reader of that article, in that journal, to know. Some history on the coining and first uses of the word infraparticle (the meaning of the root words is obvious) would also be helpful. Why don't you try drafting an introduction along these lines?—Finell 02:13, 23 February 2010 (UTC)

Finell, ok., it seems that the dispute has been resolved. Now, I won't be able to spend much time on this. Unlike me, Likebox has already read the articles on this subject in detail and he seems to have more time for Wikipedia than I have. Also he knows much more about QFT than I do. So, I see no reason why you cannot work with Likebox on this matter. Perhaps get BenRG involved here as he's also very knowlegable in QFT. It may be unhealthy if you have only one expert editor contributing to an article... Count Iblis (talk) 15:43, 23 February 2010 (UTC)

Edit request

{{Editprotected}} Could an admin please add {{Quantum-stub}} and {{Electromagnetism-stub}} to the article?--Rockfang (talk) 09:28, 22 February 2010 (UTC)

Seems uncontroversial.  Done — Martin (MSGJ · talk) 12:15, 22 February 2010 (UTC)

Citation needed for what?

I just read the previous version of this article saved in the article history [3]. I cannot find anything that is unsourced. Can somebody please point to me what part is unsourced? ScienceApologist (talk) 10:16, 22 February 2010 (UTC)

Exactly! --Michael C. Price ^talk 12:32, 22 February 2010 (UTC)

Okay, then I propose to resolve this matter by restoring that version. Unless someone objects. ScienceApologist (talk) 12:48, 22 February 2010 (UTC)

I of course agree, and I hope that this article is protected. Meanwhile, I think we all should get to work on some changes at Wikiproject physics.Likebox (talk) 14:19, 22 February 2010 (UTC)

I object, at least until we can verify that the sources are appropriate. The mere presence of sources is not enough in this case, since these were apparently deceptively added to make a point rather than to support the article (see above discussions). If the sources turn out to support the article, it can be restored to the old version, if not, these sources need to be purged from it and the improperly sourced content removed. I'll be at university later this afternoon, so I'll be able to check on them in a few hours. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 15:09, 22 February 2010 (UTC)

Your repeated assertions of deceptive sourcing, a form of vandalism, without a shred of evidence constitutes a personal attack of the worst possible sort, the kind that is backed up by frivolous administrative actions. All the sources which I have checked were valid, and those that I could not check because they weren't free were corroborated by other references, other editors, or by their abstract.

The discussion of these sources misses all the interesting points about infraparticles: the rigged hilbert space, the subtle notion of "superselection sector" used in this discussion, the relation with the density of states, everything. What you were asking for is elementary quantum field theory sources. These are certainly correct (with one exception: it is possible that the Weyl reference for gauge invariance needs to be pushed back to a 1919 paper, in which case it needs to be augmented by a later paper which establishes gauge invariance as phase invariance in 192-something by someone or other, but Weyl is definitely the original discoverer of gauge invaraince).Likebox (talk) 15:35, 22 February 2010 (UTC)

You admitted to deceptively source this article. Don't complain about the enhanced scrutiny as a result of this. This article can be kept a stub for a little while longer so we can check the sources. When in doubt, err on the cautious side. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 16:08, 22 February 2010 (UTC)

What I "admitted" to was putting sources for what you asked for which are things which are not directly relevant to the deep issues with infraparticles. You asked for sources for statements which everybody in the field knows since forever, and this makes sourcing articles on advanced topics into a joke.Likebox (talk) 16:17, 22 February 2010 (UTC)

Headbomb, please stop this canard about the "deceptive sourcing". That claim has been debunked. Fut.Perf. ☼ 16:03, 22 February 2010 (UTC)

Well looks like this is all due to a misunderstanding. I have no objection to restoring the non-stub version now that this issue is cleared up. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 13:39, 23 February 2010 (UTC)

Can we just unprotect this article and get some progress going?

As far as I can tell the problems with the article in the original state were mainly with sourcing, style and exposition, not with content. The article was written without any sourcing in an very expository style, which creates the suggestion the the ideas are original to the author. This is bad for a gazzilion reasons, but deleting the content and editprotecting the article is counter productive. The topic, although somewhat obscure, seems fairly valid and there is literature around to improve it. Some of the deleted content could quite probably be improved to get a good article from this. (Although, I see some problem with 60% percent of the article talking about Noether's theorem instead of infraparticles.) TimothyRias (talk) 15:29, 23 February 2010 (UTC)

Agreed. And so is everybody else, it seems. So who's going to unprotect it? --Michael C. Price ^talk 17:10, 23 February 2010 (UTC)

I'll ask someone on IRC. Should happen in a couple of seconds. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 17:12, 23 February 2010 (UTC)

 Done. I've restored the non-stub version as well. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 17:29, 23 February 2010 (UTC)

Great stuff. Perhaps we can carry on improving the language now. Some of the linked articles are in a bad way and need further clarification, for instance superselection sector. If that were improved then this article would make more sense as well. --Michael C. Price ^talk 17:45, 23 February 2010 (UTC)

The real issues with the text

There are real issues with this text that need to be sorted out. I didn't want to bring them up until the administrative stuff was cleared up.

1. The Noether theorem argument is old, but it is not clear that it establishes real superselection sectors: states where a charged particle is moving with different momentum are definitely different in an infinite number of soft-photons, so that this definition of superselection sector is satisfied, but you can scatter a charged particle into a different momentum state, so the definition that "no local operator can link two superselection sectors", which was Wigner's original definition, is not satisfied in any obvious way. This is a contentious point.
2. The Rigged Hilbert space: U(1) gauge theory does not have a scattering matrix, and it's hilbert space has a different structure than usual, hence infraparticles. The structure of the object which replaces the S-matrix in this context is not clear to me, and I don't even know if there is literature resolving this. It might be possible to have an S-matrix for electrodynamics on Anti-de Sitter space, but I haven't seen a source on this, nor worked it out.

These issues are real disputes in the literature, and should be represented. I have not done so, because I am not an expert on the subject, and I have not done a comprehensive literature review. I would be willing to do so at some point.Likebox (talk) 22:40, 23 February 2010 (UTC)

I also think the lead has to be cleared up a bit. It is not so clear from the lead alone what the difference is with the way charged particles are usually treated in QFT. So, I would suggest some more detail on how the infrared divergences are usually treated (that can be eleborated on later) like small mass term for photons. Then one has to make clear that by regularizing things in this way, an essential feature of charged particles in an infinite volume will always be missed. Count Iblis (talk) 00:13, 24 February 2010 (UTC)

That does raise the interesting question of what happens as you relax the infrared regulator. I presume there should be lots and lots of resonances (perhaps unstable) consisting of soft photons togetehr with the charged particle, otherwise it is hard to imagine how the density of states becomes a power law at zero photon mass. But I can't see what these quasi-bound states would look like. I wonder if this is adressed in the literature.Likebox (talk) 03:52, 24 February 2010 (UTC)

Hi everybody. I'll be honest, I have no clue what this article is talking about. The first sentence almost seems to make sense, but after that it be comes a mess of jargon and links to other articles which are equally confusing.

When constructing an article, I usually get the simple stuff out of the way first; the lede. In the lede, imagine you're trying to explain what an infraparticle is to someone like me, who has no background knowledge of this what-so-ever. Try to explain it in the simplest of terms, as if talking to a 12 year old child. Links shouldn't be necessary in the lede. Assume that I have some idea of what a photon is, but maybe clarify that I'm reading about a subatomic particle here. The lede should be one to three paragraphs, the shorter the better, and look something like what I'd expect to find in a dictionary, answering only the question, "What is an infraparticle?" When done reading it, I should feel like now I can go bore my buddies down at the bar with some new found knowledge.

After the lede, I'd make an introduction section. The intro is really just an expanded lede, written at about a tenth grade (17 year old) level. It should be about three to seven paragraphs long, and cover the entire article. Typically, I'd write a paragraph to cover each following section.

The first paragraph of the intro section is usually an intro paragraph, similarly, covering that entire section. Once this paragraph is written, the entire layout for the intro section will be revealed. Consequently, the layout for the entire article will also be revealed, (which is why writers usually start this way). The intro is the best place to start leaving links. When done reading the intro section, I should feel that I have a pretty good understanding of the subject.

The college level stuff usually comes in the following sections. Math included. Each section is usually written in the same format, that is, intro paragraph, content paragraphs, summary paragraph. (A summary is often, but not always, some type of example or application.) For that matter, each paragraph should use much the same format; intro sentence, content sentences, and summary sentence. (Think of it as a fractal pattern of writing, repeating itself on ever smaller scales.) I wrote the section liquid#Applications partly as sort of an example of what this looks like. I hope that helps. Zaereth (talk) 23:31, 6 March 2010 (UTC)

This article is on a topic which is advanced enough that if the links in the lead don't mean anything to you, then it is pointess to learn about it, you should learn about the linked things first. It's like chain rule, you need to know what a "function" is in order to appreciate it. I think that for topics like this, it's ok to jump in at a high level.Likebox (talk) 07:11, 7 March 2010 (UTC)

I agree with Zaereth, the lead needs improvement. I get as far as the end of the 1st paragraph before it becomes incomprehensible. There is no need for the article to be this badly written. (I've tried reading superselection, but that is badly written as well.). --Michael C. Price ^talk 08:48, 7 March 2010 (UTC)

I agree about superselection, but I find this article clear as day. The reason is that this article has physical pictures, while superselection is annoyingly formal.Likebox (talk) 08:55, 7 March 2010 (UTC)

It's the example they give that really fucks me up. Is it correct? The wavefunction seems many-valued! --Michael C. Price ^talk 09:49, 7 March 2010 (UTC)

It's a not fully representative example, but for other reasons--- yes the wavefunction is multivalued, but this is not an essential problem. This is just "Bloch states", periodic potential. The two ways to fix the multivaluedness are to just open up the circle into an interval, and define the closed-circle boundary condition to have a phase, or (equivalently) to say that the particle is charged and there is a magnetic vector potential parallel to the loop, making what is usually called a "flux line" or "Wilson line" of a certain magnitude. The discussion is too terse.

The real reason this is a bad example is because this is a topological superselection sector, and it is not clear that it is a superselection sector in the same sense as the other examples. The best examples are different vacua in a symmetry breaking model, states which differ in the total electric charge in a non-Higgsed electromagnetism, states of different total "fermionicity", the average position of domain wall defects in 3+1d field theory (not strings--- they flop around too much to have a well-defined average position--- that's the Mermin-Wagner theorem--- also this is a special case of symmetry breaking), D-brane positions/moduli spaces of vacua in supersymmetric theories, and least of all the topological stuff.

To understand superselection sectors really, you really have to think about the path integral, and statistical mechanics. The concept is clearer in the statistical version of the theory. Consider a big crystal sitting in space. If the crystal initialy partitions the space into cubes which are initially somewhere, then the average position of the cubes is never going to change, even though all the atoms keep fluctuating. There is exactly zero probability that the atoms will all fluctuate together, moving the crystal cubes anywhere else. Any local push or pull on the crystal is not going to move it if it is large enough.

In the quantum mechanical path-integral version, every local operator has no matrix elements between different crystal positions, so that the crystal positions define super-selection sectors.

All local operators in a non-higgsed vacuum are gauge invariant, so they have no matrix elements between states of different charge. They are not translationally invariant, so they have matrix elements between states of different momentum. So momentum is not a superselection sector, but charge is. No local operator has a matrix element between states of different position of a 2+1-d domain wall or a crystal. No local observable operator has a matrix element between states of different "Fermionness", meaning there are no local Fermionic observables (this is a different type of superselection sector too, because there are local fields which are Fermionic, they just aren't observable).

So I would say that you should think of different kinds of superselection sectors: states with infinitely many particles, states with different vaues of a broken symmetry, states with different fermionicity, states with different charge, and states with different topology. The different momentum states of infraparticle are just the silliest kind of superselection sector, states with infinitely many particles, as far as I can see. You can definitely kick a charged particle to have a different momentum with a local operator.Likebox (talk) 16:37, 7 March 2010 (UTC)

Hi Likebox. In response to your above comment to me, I didn't say that links couldn't be in the lede. Sometimes, it is necessary. I'm merely offering up some basic writing techniques, per your request on User Talk:Jimbo Wales. I'd typically try to write a lede as if writing an entry for a paper dictionary. You may think the simplifying of complex ideas to be far easier and mundane than proofing the math, but I can assure you that it is not. I'd be happy to help with this task, but can't offer more than writing advice without assistance.

To give an example of a very complex subject that I've been working to simplify is the article Basic fighter maneuvers. This is an extremely complicated subject, but the goal of such an article is to make it understandable to just about anyone who is interested in airplanes, and not just fighter pilots. At the same time, I hope it would be accurate enough that the flight instructors could make use of it as well. This takes a great deal of effort and consideration in the method choosing and assembling words. Zaereth (talk) 19:54, 8 March 2010 (UTC)

Bremsstrahlung --> Hawking radiation

Up above this comment is the evidence of a huge edit war, from Jan-Feb 2010. The current article seems to be fine to me: it explains a concept that is of continuing interest, and challenging to students of QFT. I like it, its a good article.

To the best of my incomplete knowledge, it can be extended: at least a part of Hawking radiation and of Unruh radiation can be understood as the Bremsstrahlung of infraparticles. To the best of my knowledge, one can go deeper still, and reinterpret the classical polarization density of a charged particle in classical media as the vacuum polarization (so that the vacuum looks like "media" and experiences conventional "polarization".) The analog of Bremsstrahlung during acceleration then becomes plain-old pair creation, (manifesting as Unruh radiation). I believe that it is possible for the explanation given in this article to be extended to this "polarization density", which gives gives a (semi-)classical (non-quantum) explanation to the shedding of soft particle radiation in accelerated frames. (I call it "non-quantum", because there are no one-loop diagrams, because there's no perturbative calculation that is needed to obtain the result. You can get this with "tree-level" diagrams, albeit infinite trees, due to the infrared divergence.) I do not have references to establish the above, but (to the best of my knowledge) this is all "well-known" to people working on Unruh/Hawking radiation type stuff. I'd love to see the actual calculation, as it would clarify an otherwise opaque idea. 67.198.37.16 (talk) 20:36, 22 May 2024 (UTC)