# Massless electric charges

1. Jan 22, 2006

### pseudovector

I've been studying the Yang-Mills theory, which predicted the existence of massless charged particles. That theory was later proven to be wrong, but it made me wonder nevertheless - can there ever be massless charged particles? And if such particle exists, how will it behave? How will it interact with electromagnetic fields?

2. Jan 22, 2006

### z0r

By massless, one would expect you mean "rest mass." In that case, the particle would probably behave most like a photon, traveling at speed c in free space.

Unlike a photon, however, such a particle would be affected by electromagnetic fields. One could only speculate, but I imagine if the particle were traveling through a field E which would do work on the particle, the energy and momentum of the particle would change in such a way as to increase (or decrease) the frequency (a photon with a variable wavelength, so to speak). That's just gut feeling though...

Perhaps a treatment with QM could reveal some answers.

3. Jan 23, 2006

### pseudovector

By "massless" I did mean "rest mass zero". Also, in addition to the particle's interaction with electric fields, I considered its interaction with magnetic fields, and my guess is that such particle would come to a half in the presence of magnetic fields.
But the thing that bothers me most is the fact that no such particle has been observed (as far as I know), so there has to be some law prohibiting the existance of such particles. I think it has something to do with the "optic boom" such particle will make, similar to the sonic boom caused by objects that travel at the speed of sound. This also means that such particle could feel its own electric field.

4. Jan 23, 2006

### dextercioby

I think it's an open matter. It involves the existence of consistent cross-couplings between a massless gauge abelian one-form field and an arbitrary massless field and then interpreting the nonzero coupling constant as the particle's electric charge. Something could however go wrong: the appearance of consistent self couplings of the massless field resulting in the appearence of a mass term...

Daniel.

5. Jan 24, 2006

### arivero

There was a fundamental work by Coleman and Eric Weinberg in the early seventies where they show that massless scalar electrodynamics does not exist; I do not know if the fermionic case is too trivial or too difficult.

6. Jan 24, 2006

### samalkhaiat

7. Jan 25, 2006

### dextercioby

Arivero, either way, i'll make the calculations. One thing's certain, though:it's not difficult at all to obtain a result.

Daniel.

8. Jan 25, 2006

### arivero

You need to get a copy of Sidney Coleman and Erick Weinberg "Radiative Corrections as the Origin of Spontaneous Symmetry Breaking", Phys. Rev. D 7, 1888–1910 (1973), which is -as I told- about scalar massless charged particles. The file is available from prola, http://prola.aps.org/abstract/PRD/v7/i6/p1888_1 , to aps subscribers.

9. Jan 25, 2006

### Hans de Vries

There's a follow-up on this from Weinberg together with Eldad Gilderner:

Symmetry Breaking and Scalar Bosons
Phys. Rev. D 13, 3333–3341 (1976)

But then, the relatively low Higgs boson masses predicted in this later
document (including the "scalon") have not been found.

Regards, Hans

10. Jan 26, 2006

### pseudovector

I'll look up that article. Thanks for your help.

11. Feb 2, 2006

### samalkhaiat

On the one hand there is the experimental fact; "we see mass without charge, but no electric charge without mass", on the other hand, theoretically, 4 dimensional, massless QED with invariant vacuum is possible. That is, theoretically, nothing wrong with massless fermions.
Weinberg-Witten theorem;
Limits on massless particles,
Phys. Lett. B96 (1980), 59-62.
puts sharp restrictions on the possible massless field, they cannot be completely arbitrarly as you suggest.
Basically, In dimension $n\geq4$, the spin of a massless particle is classified by a representation of the little group SO(n-2). If a local, conserved, symmetric and gauge-invariant stress tensor exists, the allowed representations for massless fields are the spinor representation(s)[there are two of these if n is even and one if n is odd], and the exterior powers of the fundamental (n-2)-dimensional representation including the trivial(scalar) representation.The theorem shows that Poincare invariant global charges vanish except for massless particles in the trivial or spinor representation;($j=0,\pm1/2$).
Without adjusting some parameters to make the particles massless, Massless particles must be massless for a reason.One possible reason is supersymmetry. But there are othere possible reasons;
Scalar particles are massless when there is a broken symmetry(Goldstone).
Fermions in four dimension are massless when they are chiral, that is, when there is unbroken chiral symmetry.
If the massless, spin1/2, particles transform in a representation$R$ of some unbroken symmetry group G, then the massless particles of spin(-1/2) transform, according to the CPT theorem, in the conjugate representation $R^*$. If $R$ and $R^*$ are distinct, then this spectrum cannot be perturbed in a G-invariant way to give masses to the fermions. So, nothing will "go wrong" and you wont get a mass term.
This shows that massless QED is possible, that is, we cannot, using the tools of QFT, show that massless charged fermions do not exist.

However, the question, which I donot know the answer to, is; Is classical electrodynamics of massless charge possible?

regareds

sam

Last edited: Feb 2, 2006
12. Feb 2, 2006

### samalkhaiat

It is neither trivial nor difficult. It is impossible to show that massless QED does not exist. see post#11.
There is the so-called Schwinger model. It is the 2-dimensional massless QED. It is exactly solvable and physically equivalent to the 2-dimensional free masive vector field theory, as found by Schwinger;

J. Schwiger, Phys. Rev. 128, 2425(1962).

regards

sam

13. Feb 3, 2006

### CarlB

Classically, if you boost the electric field of a stationary (massive) electrically charged particle, you get a magnetic field. I think I've seen speculation that the natural massless charged particles are therefore magnetic monopoles, but I don't recall where.

Carl

14. Feb 10, 2006

### samalkhaiat

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Can anybody explain to me the physics (if any) in the above quote?
I just can not understand what he is saying!

regards

sam