The Causal Function in Many Body Problems

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Abstract
Analytic properties of the causal Green's function in statistical mechanics are investigated. It is shown that the causal function can be obtained as a certain limit of an analytic function. The dual field introduced by Umezawa and Takahashi in their field‐theoretical formulation of statistical mechanics (thermo field dynamics), plays an important role to make the spectral functions real. In a few examples, it is shown explicitly that the Feynman diagram technique is applicable in the thermo‐field dynamics.