RELATIVISTIC GAUGE CONDITIONS IN QUANTUM COSMOLOGY

This paper studies the quantization of the electromagnetic field on a flat Euclidean background with boundaries. One-loop scaling factors ar e evaluated for the one-boundary and two-boundary backgrounds. The mod e-by-mode analysis of Faddeev-Popov quantum amplitudes is performed by using zeta-function regularization and is compared with the space-tim e covariant evaluation of the same amplitudes. It is shown that a part icular gauge condition exists for which the corresponding operator mat rix acting on gauge modes is in diagonal form from the beginning. More over, various relativistic gauge conditions are studied in detail, to investigate the gauge invariance of the perturbative quantum theory.