Gauge-averaging functionals for Euclidean Maxwell theory in the presence of boundaries

This paper studies the one-loop expansion of the amplitudes of electromagnetism about flat Euclidean backgrounds bounded by a 3-sphere, recently considered in perturbative quantum cosmology, by using zeta-function regularization. For a specific choice of gauge averaging functional, the contributions to the full zeta(0) value owed to physical degrees offreedom, decoupled gauge mode, coupled gauge modes, and Paddeev-Popov ghost field are derived in detail, and alternative choices for such a functional are also studied. This analysis enables one to get a better understanding of different quantization techniques for gauge fields and gravitation in the presence of boundaries