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 ζ-function regularization. For a specific choice of gauge-averaging functional, the contributions to the full ζ(0) value owed to physical degrees of freedom, decoupled gauge mode, coupled gauge modes and Faddeev-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. PACS numbers: 0370, 0460