Scalar made from electromagnetic four potential

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SUMMARY

The discussion focuses on the physical meaning of the scalar derived from the inner product of the electromagnetic four-potential, represented as gαβAαAβ. This scalar functions as a mass term for the electromagnetic field, particularly evident in superconductors where it contributes to the Meissner-Ochsenfeld effect. Additionally, the scalar's gauge dependence is highlighted, along with its relation to the canonical momentum replacement p → (p − eA) in the Hamiltonian framework for charged particles.

PREREQUISITES
  • Understanding of electromagnetic four-potential
  • Familiarity with the Meissner-Ochsenfeld effect
  • Knowledge of gauge theory in physics
  • Basic concepts of Hamiltonian mechanics
NEXT STEPS
  • Research the implications of gauge dependence in electromagnetic theory
  • Study the Meissner-Ochsenfeld effect in superconductors
  • Explore the role of canonical momentum in Hamiltonian mechanics
  • Investigate the mathematical formulation of electromagnetic four-potential
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Physicists, particularly those specializing in electromagnetism and condensed matter physics, as well as students and researchers interested in the theoretical aspects of superconductivity and gauge theories.

sweet springs
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Hi.

What physical meaning does scalar made from inner product of electromagnetic four potential, gαβAαAβ, have?

Regards.
 
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It is kind of a mass term for the electromagnetic field, which appears e.g. in superconductors where it produces the Meissner Ochsenfeld effect.
However, it is gauge dependent.
 
Hi, thank you DrDu.
Is it is related to canonical momentum replacement p → (p − eA) in Hamiltonian for charged particles ?
Regards. 
 

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