Gauge fields at finite temperatures—“Thermo field dynamics” and the KMS condition and their extension to gauge theories

Abstract

“Thermo field dynamics,” allowing the Feynman diagram method to be applied to real-time causal Green's functions at finite temperatures ( not temperature Green's functions with imaginary times) expressed in the form of “vacuum” expectation values, is reconsidered in light of its connection with the algebraic formulation of statical machanics based upon the KMS condition. On the basis of so-obtained general basic formulae, the formalism is extended to the case of gauge theories, where the subsidiary condition specifying physical states, the notion of observables, and the structure of the physical subspace at finite temperatures are clarified.