Dual Bosonic Thermal Green Function and Fermion Correlators of the Massive Thirring Model at a Finite Temperature

TL;DR

This paper derives explicit series expressions for fermionic correlators in the massive Thirring model at finite temperature by analyzing the dual bosonic thermal Green function and employing conformal mapping techniques.

Contribution

It introduces a novel approach to express fermionic correlators in the massive Thirring model using the dual bosonic Green function and complex analysis methods.

Findings

Explicit series expressions for fermionic correlators obtained.

Dual Green function identified as the imaginary part of a conformally mapped analytic function.

Method provides a new way to analyze finite-temperature correlators in 2D quantum field theories.

Abstract

The Euclidian thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space is written as the real part of a complex analytic function of a variable that conformally maps the infinite strip $-\infty<x<\infty$ ($0<\tau<\beta$) of the $z=x+i\tau$ ($\tau$: imaginary time) plane into the upper-half-plane. Using this fact and the Cauchy-Riemann conditions, we identify the dual thermal Green function as the imaginary part of that function. Using both the thermal Green function and its dual, we obtain an explicit series expression for the fermionic correlation functions of the massive Thirring model (MTM) at a finite temperature.