Scalar made from electromagnetic four potential

[sweet springs]

Hi.

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

Regards.

 

[DrDu]

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.

 

[sweet springs]

Hi, thank you DrDu.
Is it is related to canonical momentum replacement p　→　(p − eA) in Hamiltonian for charged particles ?
Regards.