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A quantum field theory at finite temperature is presented. The temperature dependent vacuum is defined such that the vacuum expectation value agrees with the statistical average. The vacuum states with different temperature are connected by a Bogoliubov transformation. Our formalism allows the use of the Feynman diagrams for the causal Green’s function and the Bethe-Salpeter technique for bound states at finite temperature, The entropy operator is introduced.
Takahashi et al. (Sun,) studied this question.