LIMITATIONS OF GAUGE INVARIANCE

PHYSICAL GAUGE
Electrostatics can be formulated self-consistently with scalar potentials
alone. Any gauge transformation will preserve the particle trajectory,
but will introduce some unphysical feature such as the failure of energy
conservation. Implication: there exists a gauge that is entirely physical.
For electrostatics, the physical gauge is the gauge with only a scalar
potential and no vector potential.
0, A = 0
Static (and quasistatic) fields are called longitudinal fields.
The electric field follows field lines from one plate of a parallel plate
capacitor to the other. This can be viewed as the “propagation” of the
electric field in a direction parallel to the polarization direction.
Any gauge transformation from the physical gauge introduces some
feature(s) that are nonphysical,
even though gauge invariance holds true.
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