Quantum electrodynamics without potentials

A scheme is proposed for quantizing electrodynamics in terms of the electromagnetic fields without the introduction of potentials. The equations are relativistically covariant and do not require the introduction of unphysical states and an indefinite metric. Calculations carried out according to current quantization methods in the Coulomb or Lorentz gauges are justified in the new formalism. The theory exhibits an analogy between phases of operators and electromagnetic fields on the one hand, and coordinate systems and space curvature on the other. It is suggested that this analogy may be useful in quantizing the gravitational field.