Stochastic Quantization and Casimir Forces

TL;DR

This paper introduces a stochastic quantization approach to compute Casimir forces, incorporating quantum and thermal fluctuations, and deriving the force directly from the stress tensor for arbitrary geometries.

Contribution

It presents a novel method using stochastic quantization to calculate Casimir forces directly from the stress tensor, including force fluctuations, applicable to complex geometries.

Findings

The method accurately computes Casimir forces in arbitrary geometries.

Force fluctuations are explicitly derived, showing variance twice the force squared in piston cases.

The approach simplifies calculations by using spectral decomposition of the Laplacian.

Abstract

In this paper we show how the stochastic quantization method developed by Parisi and Wu can be used to obtain Casimir forces. Both quantum and thermal fluctuations are taken into account by a Langevin equation for the field. The method allows the Casimir force to be obtained directly, derived from the stress tensor instead of the free energy. It only requires the spectral decomposition of the Laplacian operator in the given geometry. The formalism provides also an expression for the fluctuations of the force. As an application we compute the Casimir force on the plates of a finite piston of arbitrary cross section. Fluctuations of the force are also directly obtained, and it is shown that, in the piston case, the variance of the force is twice the force squared.