General Gauge Invariance Problem

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SUMMARY

The discussion centers on proving that the amplitude of the process γγ → W⁺W⁻ is independent of the chosen gauge, specifically the Rₓ gauge. The user identifies five diagrams involved in the calculation, including one with only the four fields and a vertex, and others utilizing W bosons and a non-physical field φ as propagators. The challenge arises in simplifying the expressions to eliminate gauge dependence, particularly when incorporating the Goldstone boson associated with the Rₓ gauge. Clarification is sought regarding the nature of the non-physical field, which is identified as a charged Goldstone boson.

PREREQUISITES
  • Understanding of gauge invariance in quantum field theory
  • Familiarity with Feynman diagrams and their interpretation
  • Knowledge of Rₓ gauge and its implications
  • Concept of Goldstone bosons and their role in particle physics
NEXT STEPS
  • Study the derivation of gauge invariance in quantum electrodynamics
  • Learn about the role of Goldstone bosons in the Higgs mechanism
  • Explore Feynman diagram calculations involving non-physical fields
  • Investigate the implications of gauge choices on physical observables
USEFUL FOR

This discussion is beneficial for theoretical physicists, particularly those specializing in quantum field theory and particle physics, as well as graduate students seeking to deepen their understanding of gauge invariance and related concepts.

llorgos
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Hi!

I have to prove that the amplitude of the process

\gamma \gamma \to W^+ W^-

does not depend on the gauge we will choose, R_{\xi}.

So I use the most general expressions for the propagators and vertices. I find 5 diagrams. One that involves only the 4 fields and a vertex, 1 t and one u channel with a W boson as propagator and 1 t and 1 u where the propagator is a non-physical field \phi.

I just sum up the last 4, since the first one does not depend on the \xi parameter but then I am stuck since nothing seems to make the horrible expressions in such a way that there will be no gauge dependence in the end..

Any help?
 
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llorgos said:
non-physical field \phi.

What is this unphysical field? - A ghost? If it is, I don't see how you make the diagram. If it's some field I don't know, please elaborate.
 
It is a goldstone boson coming around in the R_{\xi} gauge. Actually it is the charged one.
 

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