One-Loop Effective Action on the Four-Ball

Abstract

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 ${\zeta }^{\prime }(0)$ 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 ${\zeta }^{\prime }(0)$ resulting from longitudinal, normal and ghost modes.

25 pages, plain Tex

References in corpus (8)

• Euclidean Maxwell Theory in the Presence of Boundaries. II
• Further functional determinants
• Relativistic Gauge Conditions in Quantum Cosmology
• The one-loop form factors in the effective action, and production of coherent gravitons from the vacuum
• Gauge-Averaging Functionals for Euclidean Maxwell Theory in the Presence of Boundaries
• Coulomb Gauge in One-Loop Quantum Cosmology
• Heat-kernel coefficients and functional determinants for higher-spin fields on the ball
• Spin on the 4-ball

Cited by in corpus (5)

• Heat kernel expansion: user's manual
• Heat-kernels and functional determinants on the generalized cone
• One-Loop Divergences in Simple Supergravity: Boundary Effects
• Zeta function for the Laplace operator acting on forms in a ball with gauge boundary conditions
• One-Loop Effective Action for Euclidean Maxwell Theory on Manifolds with Boundary