Radiative Contributions to the Effective Action of Self-Interacting Scalar Field on a Manifold with Boundary

Abstract

The effect of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The analysis is most easily performed in a space of constant curvature the boundary of which is characterised by constant extrinsic curvature. An extension of the spherical formulation in the presence of a boundary is attained through use of the method of images. Contrary to the consolidated vanishing effect in maximally symmetric space-times the contribution of the massless "tadpole" diagram no longer vanishes in dimensional regularisation. As a result, conformal invariance is broken due to boundary-related vacuum contributions. The evaluation of one-loop contributions to the two-point function suggests an extension, in the presence of matter couplings, of the simultaneous volume and boundary renormalisation in the effective action.

14 pages, 1 figure. Additional references and minor elucidating remarks added. To appear in Classical and Quantum Gravity

References in corpus (1)

• Diagrams for heat kernel expansions

Cited by in corpus (6)

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• Spherical Formulation for Diagramatic Evaluations on a Manifold with Boundary
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• Perturbative Evaluation of Interacting Scalar Fields on a Curved Manifold with Boundary
• Conformal Anomaly for Free Scalar Propagation on Curved Bounded Manifolds
• Conformal Anomalies for Interacting Scalar Fields on Curved Manifolds with Boundary