Euclidean Maxwell Theory in the Presence of Boundaries. II

Details Euclidean Maxwell Theory in the Presence of Boundaries. II Euclidean Maxwell Theory in the Presence of Boundaries. II

1995-06-27

arxiv.org/abs/gr-qc/9506061v1

Class.Quant.Grav.11:2939-2950,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, plain-tex, recently appearing in Classical and Quantum Gravity, volume 11, pages 2939-2950, December 1994. The autho

Scientific paper

10.1088/0264-9381/11/12/009

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.

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