Canonical Quantization for a Relativistic Neutral Scalar Field in Non-equilibrium Thermo Field Dynamics

TL;DR

This paper develops a canonical quantization approach for a relativistic neutral scalar field in non-equilibrium thermo field dynamics, deriving a quantum Boltzmann equation with self-consistent radiative corrections.

Contribution

It introduces a time-dependent thermal Bogoliubov transformation and a thermal counter term, leading to a novel derivation of the quantum Boltzmann equation for non-equilibrium fields.

Findings

Derived the quantum Boltzmann equation for the scalar field.

Implemented a self-consistency renormalization condition.

Accounted for radiative corrections via a thermal counter term.

Abstract

A relativistic neutral scalar field is investigated in non-equilibrium thermo field dynamics. The canonical quantization is applied to the fields out of equilibrium. Because the thermal Bogoliubov transformation becomes time-dependent, the equations of motion for the ordinary unperturbed creation and annihilation operators are modified. This forces us to introduce a thermal counter term in the interaction Hamiltonian which generates additional radiative corrections. Imposing the self-consistency renormalization condition on the total radiative corrections, we obtain the quantum Boltzmann equation for the relativistic scalar field.