From superoperator formalism to nonequilibrium Thermo Field Dynamics

TL;DR

This paper develops a unique unperturbed representation in the superoperator formalism for nonequilibrium quantum field systems, leading to a formulation of Thermo Field Dynamics and a new renormalization condition for quantum transport.

Contribution

It introduces a novel unperturbed representation satisfying key physical requirements, generalizes the renormalization condition, and derives quantum transport equations.

Findings

Formulation of nonequilibrium Thermo Field Dynamics

Identification of inconsistencies in previous diagonalization conditions

Proposal of a new renormalization condition for self-energy

Abstract

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.