Gauge fixing in 5D vs 4D, and photon polarization

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SUMMARY

The discussion focuses on gauge fixing in 4D and 5D contexts, specifically regarding photon polarization and gauge fields. In 3+1 dimensions, the photon has two polarizations and the gauge field A_\mu has four components, necessitating the removal of two extra degrees of freedom, which the Lorentz gauge alone cannot achieve. In 4+1 dimensions, the photon maintains two polarizations, but the gauge field A_\mu has five components, requiring the elimination of three extra degrees of freedom. The Lorentz gauge is insufficient for this purpose, prompting the need for alternative gauge-fixing methods.

PREREQUISITES
  • Understanding of gauge theory and gauge fields
  • Familiarity with Lorentz gauge conditions
  • Knowledge of photon polarization and spin
  • Basic concepts of dimensional analysis in physics
NEXT STEPS
  • Research alternative gauge-fixing methods beyond the Lorentz gauge
  • Explore the implications of extra degrees of freedom in gauge theories
  • Study the mathematical formulation of gauge fields in higher dimensions
  • Investigate the role of photon polarization in quantum field theory
USEFUL FOR

The discussion is beneficial for theoretical physicists, students of quantum field theory, and researchers interested in gauge theories and higher-dimensional physics.

kuon
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I'm sorry if what I say is not right, or I haven't understood it right,

- In 3+1 D we have the photon with spin 1 => it has two polarizations.

Our Gauge field [tex]A_\mu[/tex] has 4 components => We have two extra degrees of freedom. => We need to get rid of the extra 2 fixing the gauge. 1. The Lorentz gauge is not enough to fix them. What else can we do?- In 4+1 D we have the photon with spin 1=> it has two polarizations.

Our Gauge field [tex]A_\mu[/tex] has 5 components => We have THREE extra degrees of freedom. => We need to get rid of the extra 3 fixing the gauge.

2. The Lorentz gauge is not enough to fix them. What else can we do?

Thank you very much for your attention :)
 
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kuon said:
I'm sorry if what I say is not right, or I haven't understood it right,

- In 3+1 D we have the photon with spin 1 => it has two polarizations.

Our Gauge field [tex]A_\mu[/tex] has 4 components => We have two extra degrees of freedom. => We need to get rid of the extra 2 fixing the gauge.


1. The Lorentz gauge is not enough to fix them. What else can we do?

In the Lorentz gauge there are two extra degrees of freedom which do not contribute even without getting rid of them. They cannot exchange the energy-momentum with physical degrees of freedom.
 

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