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From superoperator formalism to nonequilibrium Thermo Field Dynamics. (English) Zbl 1266.81134
Summary: Emphasizing that the specification of the representation space or the quasiparticle picture is essential in nonequilibrium quantum field system, we have constructed the unique unperturbed representation of the interaction picture in the superoperator formalism. To achieve it, we put the three basic requirements (the existence of the quasiparticle picture at each instant of time, the macroscopic causality and the relaxation to equilibrium). From the resultant representation follows the formulation of nonequilibrium Thermo Field Dynamics (TFD). The two parameters, the number distribution and excitation energy, characterizing the representation, are to be determined by the renormalization condition. While we point out that the diagonalization condition by Chu and Umezawa is inconsistent with the equilibrium theory, we propose a new renormalization condition as a generalization of the on-shell renormalization on the self-energy which derives the quantum transport equation and determines the renormalized excitation energy.

MSC:
81T28 Thermal quantum field theory
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
82C70 Transport processes in time-dependent statistical mechanics
82C35 Irreversible thermodynamics, including Onsager-Machlup theory
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