Quasi-local stress-tensor formalism and the Casimir effect

TL;DR

This paper uses a quasi-local stress-tensor approach to analyze the Casimir effect for scalar fields, confirming the zero surface energy and revealing a significant first-order correction to the Casimir energy.

Contribution

It extends the quasi-local stress-energy tensor formalism to scalar fields in Casimir setups, demonstrating a non-zero first-order correction to the energy.

Findings

Surface energy vanishes for both boundary conditions

Volume Casimir energy equals the zero point energy

First-order correction to Casimir energy is significant and detectable

Abstract

We apply the quasi-local stress-energy tensor formalism to the Casimir effect of a scalar field confined between conducting planes located in a static spacetime. We show that the surface energy vanishes for both Neumann and Dirichlet boundary conditions and consequently the volume Casimir energy reduces to the famous zero point energy of the quantum field, i.e. $E^{vol.}=\sum\frac{\hbar \omega}{2}$. This enables us to reinforce previous results in the literature and extend the calculations to the case of massive and arbitrarily coupled scalar field. We found that there exists a first order perturbation correction to the Casimir energy contrary to previous claims which state that it vanishes. This shows many orders of magnitude greater than previous estimations for the energy corrections and makes it detectable by near future experiments.