Photon helicity: Wigner's unitary rep. of Poincare group and gauge symmetry

[DrDu]

OK, I'm not familiar with the details of that. Could you give me a reference, pls?

http://jmp.aip.org/resource/1/jmapaq/v4/i6/p776_s1
especially formula V.7

 

[TrickyDicky]

One question, certainly the Poincare group and the gauge symmetry group commute, does the little group-SE(2) commute with the gauge symmetry?

 

[tom.stoer]

yes, why not?

 

[A. Neumaier]

Starting with massive vector bosons with the limit m → 0 fails in non-abelian gauge theories (afaik it breaks the SlavnovTaylor identities which indicates an anomaly, i.e. the gauge symmetry is bot restored in the limit m → 0; but I am not sure about that)

The problem in the nonabelian case is that a massive nonabelian gauge theory (without a symmetry-breaking mechanism) is not renormalizable. If nonrenormalizable theories were better understood, the massless limit would probably work out well.

 

[A. Neumaier]

I would expect an underlying principle (unfortunately unknown) which explains why gauge symmetry adds constraints to Poincare multiplets and why Casimir operators of Poincare symmetry tell something about the construction of gauge symmetries.

Gauge symmetry adds constraints to Poincare multiplets because an interaction with a gauge field can be gauge invariant only if the coupling is to a conserved current. A Fourier transform gives the transversality condition. But transversality is Poincare invariant only in massless representations.

Weinberg's paper Phys.Rev. 134 (1964), B882-B896 should explain everything to your satisfaction.

 

[time601]

the paper on arxiv(arxiv:1403.2698) maybe explain it.

 

[tom.stoer]

thanks for the hint; seems to be a new explanation based on spacetime-symmetry, but still unrelated to local gauge invariance

 

[strangerep]

the paper on arxiv(arxiv:1403.2698) maybe explain it.

I think that paper does not "explain" it any better than Weinberg. Banishment of the extra degrees of freedom (so-called "continuous spin") is still quite arbitrary. See top right of their p3 and also the last paragraph of their conclusion.

Weinberg's justification is that particles with such continuous spin degrees of freedom are not observed experimentally. Hence we arbitrarily ignore that possibility when constructing photonic quantum fields.

The justification of Chang-Li and Feng-Jun in the above paper is just as arbitrary: they seem to think that "just admitting" that certain states are unphysical is somehow different from Weinberg. They seem to think that Weinberg is using an extra "experimental hypothesis", whereas in fact he is just referring to (lack of) experimental evidence as a way to make the arbitrary exclusion reasonable.