  where \(\chi\) is a scalar function (of space and time or of space-time) which can be chosen arbitrarily. Inserting the transformed potential(s) into equation(s) (2.3), or (2.4), one can see that the electric field \(\mathbf{E}\) and the magnetic field \(\mathbf{B}\), or covariantly the electromagnetic field tensor \(F^{\mu \nu}\), are not affected by a gauge transformation of the potential(s). Since only the electric field \(\mathbf{E}\) and the magnetic field \(\mathbf{B}\), and quantities constructed from them, are observable, whereas the vector potential itself is not, nothing physical seems to be changed by a gauge transformation because it leaves \(\mathbf{E}\) and \(\mathbf{B}\) unaltered. Note that gauge invariance is a kind of symmetry that does not come about by space-time transformations.