Casimir Effect at Finite Temperature

Abstract
We investigate the spatial variation of the thermal stress energy tensor between two plane boundaries for conformally coupled massless scalar fields obeying the Dirichlet or the Neumann boundary conditions, and for two independent polarizations of the electromagnetic field obeying perfect conductor boundary condition. In particular we find the sinusoidal spatial behaviour for each field in the low temperature limit. We also discuss the fluctuation of the electromagnetic field. The electric field fluctuation is found to be positive definite, while the magnetic one is found to have nodes above a critical temperature inversely proportional to the distance between the two boundaries.

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