Longitudinal polarization in Feynman photon propagator?

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SUMMARY

The discussion centers on the necessity of summing over longitudinal polarization states in the context of internal photon states within quantum field theory. It is concluded that including longitudinal states is unnecessary since they do not couple to the conserved electromagnetic current. The ordinary Feynman-gauge propagator suffices, as the ##k^\mu k^\nu## term can be multiplied by an arbitrary number without affecting scattering amplitudes, a concept referred to as "generalized Feynman gauge."

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  • Understanding of quantum field theory principles
  • Familiarity with Feynman propagators and gauge theories
  • Knowledge of electromagnetic current conservation
  • Basic grasp of polarization states in quantum mechanics
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  • Study the implications of generalized Feynman gauge in quantum field theory
  • Explore the role of longitudinal polarization in gauge theories
  • Learn about scattering amplitudes and their dependence on gauge choices
  • Investigate the conservation laws in electromagnetic interactions
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Physicists, particularly those specializing in quantum field theory, gauge theory, and particle physics, will benefit from this discussion.

copernicus1
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For internal photon states, is it necessary to sum over the longitudinal polarization state in addition to the transverse states? And if so, does the ordinary Feynman-gauge propagator take care of this?

Thanks!
 
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No. However, the longitudinal states do not couple to the conserved electromagnetic current, so it doesn't matter whether you include them or not. Thus the ##k^\mu k^\nu## term in the propagator can be multiplied by an arbitrary number (this is sometimes called "generalized Feynman gauge"), and the scattering amplitudes do not depend on that number.
 
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