QUANTUM GAUGE EQUIVALENCE IN QED

We discuss gauge transformations in QED coupled to a charged spinor fi eld, and examine whether we can gauge-transform the entire formulation of the theory from one gauge to another, so that not only the gauge a nd spinor fields, but also the forms of the operator-valued Hamiltonia ns are transformed. The discussion includes the covariant gauge, in wh ich the gauge condition and Gauss's law are not primary constraints on operator-valued quantities: it also includes the Coulomb gauge, and t he spatial axial gauge, in which the constraints are imposed on operat or-valued fields by applying the Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb, and spatial axial gauges to what we call ''common form,'' in which all particle excitation modes have identical properties. We also show that, once that common form has bee n reached, QED in different gauges has a common time-evolution operato r that defines time-translation for states that represent systems of e lectrons and photons. By combining gauge transformations with changes of representation from standard to common form, the entire apparatus o f a gauge theory can he transformed from one gauge to another.