Gauge-Invariant Quantum Electrodynamics

Abstract

Electrodynamics is quantized without resort to subsidiary conditions. The quantization is carried out by identifying quantum commutators with the commutators of a classical transformation group related to the canonical transformations. The resulting theory is completely gauge invariant, and Maxwell's equations hold as operator equations. The quantization of both electromagnetic and electron fields is carried out in terms of gauge-invariant quantities. For the Dirac field the observables satisfy commutation relations. The anticommutation rules satisfied by the field variables must be deduced from the commutators of observables. The resulting theory is completely equivalent to the usual quantum electrodynamics.