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

• URL: http://arxiv.org/abs/2605.17124v1
• Date: Sat, 16 May 2026 19:04:18 GMT
• Title: Covariant extrinsic curvature expansion of the nonlocal effective action for a massless scalar field on a manifold with boundary
• Abstract summary: We study the nonlocal effective action of a massless scalar field defined on a flat manifold with a curved boundary.<n>We derive a covariant expansion of the nonlocal contribution to quadratic order in the extrinsic curvature tensor.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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