  where \(F^{\mu \nu}\) is the electromagnetic field tensor and \(A^{\mu} = (\phi , \mathbf{A})\) the 4-vector potential. The important point in the present context is that given the identification (2.3), or (2.4), there remains a certain flexibility or freedom in the choice of \(\mathbf{A}\) and \(\phi\), or \(A^{\mu}\). In order to see that, consider the so-called gauge transformations