  A gauge transformation in quantum electrodynamics involves the product of
field operators at the same space-time point and hence does not have a
well-defined meaning. One way to avoid this difficulty is to generalize the
gauge transformation by using different space-time points in the spirit of
Dirac's point splitting. Such a generalization indeed exists and the resulting
infinitesimal gauge transformation takes the form of an infinite series in the
coupling constant. In this text I will present two examples of generalized
gauge transformations.
