Stochastic quantization and Casimir forces
Departamento de Física Aplicada I and GISC, Universidad Complutense - 28040 Madrid, Spain, EU
2 Departamento de Física, FCFM, Universidad de Chile - Casilla 487-3, Santiago, Chile
Accepted: 18 October 2011
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 03.70.+k – Theory of quantized fields / 42.50.Lc – Quantum fluctuations, quantum noise, and quantum jumps
© EPLA, 2011