Non-Equilibrium Thermo Field Dynamics for Relativistic Complex Scalar and Dirac Fields

TL;DR

This paper develops a non-equilibrium thermo field dynamics framework for relativistic complex scalar and Dirac fields, deriving quantum Boltzmann equations through self-consistent thermal self-energy analysis.

Contribution

It introduces a novel approach using Bogoliubov transformations with independent parameters for charged fields, leading to derivation of quantum Boltzmann equations.

Findings

Thermal vacuum defined via Bogoliubov transformations.

Self-consistency renormalization fixes thermal counter terms.

Quantum Boltzmann equations derived for relativistic fields.

Abstract

Relativistic quantum field theories for complex scalar and Dirac fields are investigated in non-equilibrium thermo field dynamics. The thermal vacuum is defined by the Bogoliubov transformed creation and annihilation operators. Two independent Bogoliubov parameters are introduced for a charged field. Its difference naturally induces the chemical potential. Time-dependent thermal Bogoliubov transformation generates the thermal counter terms. We fix the terms by the self-consistency renormalization condition. Evaluating the thermal self-energy under the self-consistency renormalization condition, we derive the quantum Boltzmann equations for the relativistic fields.