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

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Abstract
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 -function regularization. For a specific choice of gauge-averaging functional, the contributions to the full 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.
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