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arXiv · 2605.17124

Covariant extrinsic curvature expansion of the nonlocal effective action for a massless scalar field on a manifold with boundary

A. Boasso·C. D. Fosco·B. C. Guntsche·F. D. Mazzitelli
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Abstract

We study the nonlocal effective action of a massless scalar field defined on a flat manifold with a curved boundary. Using a heat-kernel approach, we derive a covariant expansion of the nonlocal contribution to quadratic order in the extrinsic curvature tensor. Our construction provides a geometric framework that both reproduces earlier results obtained for Monge-patch embeddings and extends them to more general surfaces that need not admit a global Monge-patch description. The expansion is valid in the regime where gradients of the extrinsic curvature dominate over nonlinear curvature effects. As an application, we compute the particle-creation rate for an oscillating deformed ring in $2+1$ dimensions and an oscillating deformed sphere in $3+1$ dimensions.

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A. Boasso, C. D. Fosco, B. C. Guntsche, F. D. Mazzitelli. 2026-05-16. Covariant extrinsic curvature expansion of the nonlocal effective action for a massless scalar field on a manifold with boundary. https://arxiv.org/abs/2605.17124

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