The Casimir Effect at Nonzero Temperature
This chapter considers Casimir energy not in the vacuum state of a quantum field in the presence of boundaries but in a state containing real particles in thermal equilibrium. In fact, an ensemble of states characterized by a temperature T and a probability distribution is considered. In quantum field theory there exist several methods to treat a system at nonzero temperature. The easiest and most frequently used method is the imaginary-time Matsubara formalism. It is applied to find a general finite expression for Casimir free energy. Asymptotic expressions for the Casimir free energy are obtained in the cases of low and high temperature. The coefficients of the high-temperature expansion are expressed in terms of the heat kernel coefficients.
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