In order to bridge between the two different gauges, we need a gauge transformation.

Since is a first class primary constraint it should be interpreted as a generator of a gauge transformation.

To see this, consider the effect of a gauge transformation on the field.

But now the phase of the field is arbitrary, because gauge transformations change it.

It is equally used for massive spin-1 fields where the concept of gauge transformations does not apply at all.

A transformation from one such field configuration to another is called a gauge transformation.

The relevant point here is that the fields remain the same under the gauge transformation, and therefore Maxwell's equations are still satisfied.

The fields remain the same under the gauge transformation, and therefore Maxwell's equations are still satisfied.

A gauge transformation is just a transformation between two such sections.

Whose variation under an infinitesimal gauge transformation is given by: