One-Loop Effective Action on the Four-Ball

Details One-Loop Effective Action on the Four-Ball One-Loop Effective Action on the Four-Ball

1996-01-03

arxiv.org/abs/hep-th/9601006v1

Class.Quant.Grav. 13 (1996) 943-956

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, plain Tex

Scientific paper

10.1088/0264-9381/13/5/013

This paper applies $\zeta$-function regularization to evaluate the 1-loop effective action for scalar field theories and Euclidean Maxwell theory in the presence of boundaries. After a comparison of two techniques developed in the recent literature, vacuum Maxwell theory is studied and the contribution of all perturbative modes to $\zeta'(0)$ is derived: transverse, longitudinal and normal modes of the electromagnetic potential, jointly with ghost modes. The analysis is performed on imposing magnetic boundary conditions, when the Faddeev-Popov Euclidean action contains the particular gauge-averaging term which leads to a complete decoupling of all perturbative modes. It is shown that there is no cancellation of the contributions to $\zeta'(0)$ resulting from longitudinal, normal and ghost modes.

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