An alternative formulation is given for the quantum theory of fields in which the charge on a particle is introduced as an operator rather than as a number. In addition to the advantage of mathematical simplicity, this formulation allows the fundamental properties of charge quantization and charge conservation to be deduced from the one hypothesis introduced to replace that of gauge invariance of the first kind. Systems of particles of different mass and charge may be treated more elegantly by this method, which is identical with the usual one for particles of spin zero, but which leads to a generalized Dirac equation which could be applied, for instance, to a mixed electron and neutrino field. This equation is very simply expressible in terms of modified field-dependent Dirac operators, and leads to oscillations of the specific charge of a particle analogous to the zitterbewegung.