Boundary divergences in vacuum self-energies and quantum field theory in curved spacetime

TL;DR

This paper investigates how boundary conditions in quantum field theory in curved spacetime cause divergences in energy-momentum tensors, and demonstrates that these divergences can be eliminated with smooth interfaces, ensuring consistent gravitational effects.

Contribution

It introduces a renormalizable model of a quantum scalar field with boundary conditions in curved spacetime, showing divergences vanish for smooth interfaces.

Findings

Divergences depend on boundary smoothness

Model is renormalizable in curved spacetime

Smooth interfaces eliminate divergences

Abstract

It is well known that boundary conditions on quantum fields produce divergences in the renormalized energy-momentum tensor near the boundaries. Although irrelevant for the computation of Casimir forces between different bodies, the self-energy couples to gravity, and the divergences may, in principle, generate large gravitational effects. We present an analysis of the problem in the context of quantum field theory in curved spaces. Our model consists of a quantum scalar field coupled to a classical field that, in a certain limit, imposes Dirichlet boundary conditions on the quantum field. We show that the model is renormalizable and that the divergences in the renormalized energy-momentum tensor disappear for sufficiently smooth interfaces.