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

Click For Summary
SUMMARY

The discussion centers on the relationship between helicity states of massless particles, specifically photons, and their representation under the Poincaré group and gauge symmetries. It establishes that for massless particles, physical states are characterized by helicity, with photons having two degrees of freedom (d.o.f.) represented by |kμ, h> where kμkμ = 0 and h = ±1. The conversation highlights that while both Poincaré invariance and gauge invariance yield the same results regarding helicity states, they do so through different methodologies, leading to questions about the underlying connection between these approaches. The discussion also touches on the implications for non-abelian gauge theories and the necessity of additional empirical input for proper classification of elementary particles.

PREREQUISITES
  • Understanding of massless particle representations in quantum field theory.
  • Familiarity with gauge theories, specifically Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD).
  • Knowledge of the Poincaré group and its role in particle physics.
  • Concepts of gauge fixing and the implications for degrees of freedom in field theories.
NEXT STEPS
  • Study the Wigner classification of massless particles and its implications for helicity states.
  • Explore gauge fixing techniques in quantum field theory, particularly in the context of QED and QCD.
  • Investigate the role of the Poincaré group in non-abelian gauge theories and the associated challenges.
  • Review Weinberg's "Quantum Field Theory" for deeper insights into the relationship between gauge symmetries and Poincaré invariance.
USEFUL FOR

Physicists, particularly those specializing in quantum field theory, gauge theories, and particle physics, will benefit from this discussion. It is also relevant for researchers exploring the foundational aspects of particle classification and the interplay between symmetries in theoretical physics.

  • #61
strangerep said:
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
 
Last edited by a moderator:
Physics news on Phys.org
  • #62
One question, certainly the Poincare group and the gauge symmetry group commute, does the little group-SE(2) commute with the gauge symmetry?
 
  • #63
yes, why not?
 
  • #64
tom.stoer said:
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.
 
  • #65
tom.stoer said:
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.
 
  • #66
the paper on arxiv(arxiv:1403.2698) maybe explain it.
 
  • #67
thanks for the hint; seems to be a new explanation based on spacetime-symmetry, but still unrelated to local gauge invariance
 
  • #68
time601 said:
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.
 

Similar threads

Graduate Any good idea how non-abelian gauge symmetries emerge?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad What Does Gauge Invariance Tell Us About Reality?
  • · Replies 2 ·
Replies
2
Views
2K
Two spin d.o.f. for massless gauge bosons
  • · Replies 29 ·
Replies
29
Views
8K
Is the Higgs mechanism a gauge transformation or not?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Minimum requisite to generalize Proca action
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What Is the Role of Gauge Theory in Particle Physics?
  • · Replies 3 ·
Replies
3
Views
2K
Model with SU(2) gauge symmetry and SO(3) global symmetry
  • · Replies 1 ·
Replies
1
Views
2K
Representations of the Poincare group
  • · Replies 2 ·
Replies
2
Views
3K
Modifying photon states to get a gauge symmetry
  • · Replies 7 ·
Replies
7
Views
2K
Understanding Gauge Symmetry in Massive Gravity: Analysis of Fierz-Pauli Action
  • · Replies 47 ·
2
Replies
47
Views
5K