Two-Dimensional Thermofield Bosonization

TL;DR

This paper develops an operator-based bosonization method for 1+1 dimensional fermions at finite temperature using Thermofield Dynamics, extending zero-temperature results and simplifying calculations compared to traditional formalisms.

Contribution

It provides a new operator realization for finite-temperature bosonization in 1+1 dimensions, demonstrating the persistence of fermion-boson correspondence at non-zero temperature.

Findings

Bosonization at finite temperature parallels zero-temperature case.

Operator realization simplifies calculations over traditional formalisms.

Transmutation from Fermi-Dirac to Bose-Einstein statistics is explicitly shown.

Abstract

The main objective of this paper is to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real time formalism of Thermofield Dynamics. Formally the results parallel those of the T = 0 case. The well known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. In order to emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized.