Euclidean Maxwell Theory in the Presence of Boundaries. II

TL;DR

This paper applies zeta-function regularization to analyze the quantized electromagnetic field with boundaries, demonstrating gauge independence of one-loop amplitudes in certain boundary configurations and highlighting issues with gauge dependence in others.

Contribution

It provides a detailed calculation showing gauge independence of quantum amplitudes with two concentric spherical boundaries and discusses gauge dependence issues with a single boundary.

Findings

One-loop amplitudes are gauge independent with two concentric spheres.

Mode-by-mode evaluation matches covariant formulae.

Gauge dependence appears with a single boundary sphere.

Abstract

Zeta-function regularization is applied to complete a recent analysis of the quantized electromagnetic field in the presence of boundaries. The quantum theory is studied by setting to zero on the boundary the magnetic field, the gauge-averaging functional and hence the Faddeev-Popov ghost field. Electric boundary conditions are also studied. On considering two gauge functionals which involve covariant derivatives of the 4-vector potential, a series of detailed calculations shows that, in the case of flat Euclidean 4-space bounded by two concentric 3-spheres, one-loop quantum amplitudes are gauge independent and their mode-by-mode evaluation agrees with the covariant formulae for such amplitudes and coincides for magnetic or electric boundary conditions. By contrast, if a single 3-sphere boundary is studied, one finds some inconsistencies, i.e. gauge dependence of the amplitudes.