Vacuum Stress between Conducting Plates: An Image Solution

Abstract

The zero-point fluctuations of the electromagnetic field give rise to an attractive force between two perfectly conducting parallel plates, the Casimir force. We discuss the structure of the electromagnetic stress-energy tensor in the region between the plates for finite temperatures as well as for the zero-temperature limit, and we describe the relationship of its components to the thermodynamic variables of the radiation field. The stress-energy tensor is defined so that infinite quantities never appear, and it is explicitly computed with the aid of an image-source construction of the Green's function. The finite-temperature case involves both an infinite set of spatial images and an infinite sum of temperature-dependent images.