Coulomb Gauge in One-Loop Quantum Cosmology

The well-known discrepancies between covariant and non-covariant formalisms in quantum field theory and quantum cosmology are analyzed by focusing on the Coulomb gauge for vacuum Maxwell theory. On studying a flat Euclidean background with boundaries, the corresponding mode-by-mode analysis of one-loop quantum amplitudes agrees with the results of the Schwinger-DeWitt technique and of mode-by-mode calculations in relativistic gauges.