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

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 thatplane 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.

Obtaining a closed-form representation for the dual bosonic thermal Green function by using methods of integration on the complex plane

“…This dual thermal Green function turns out to be a key ingredient for the obtainment of fermion correlators of the MTM at finite temperature, as shown in Ref. [5].…”

“…The peculiar form of this, allows us to easily recognize it as the real part of an analytic function, a fact that leads us to determine the corresponding dual thermal Green function as the imaginary part of that function, according to the Cauchy-Riemann conditions. This dual thermal Green function turns out to be a key ingredient for the obtainment of fermion correlators of the MTM at finite temperature, as shown in [5].…”

Vanishing conductivity of quantum solitons in polyacetylene

“…( 10) implies that the operator µ creates eigenstates of the topological charge Q, with eigenvalue 2π/N, thus proving that the quantum solitons occurring in the theory described by ( 1) are indeed phase solitons. Correlation functions of these quantum soliton excitations have been calculated elsewhere [10,11,12]. In Section 4, we will show that the relevant quantum correlators for the calculation of the conductivity will be the soliton current-current correlators.…”

Thermal Soliton Correlation Functions in Theories with a <i>Z</i>(N) Symmetry

“…In this work we employ the same methodology established in [5] in order to obtain an explicit series expression for the two-point thermal soliton correlation function in theories with a Z(N) symmetry. This has been done, firstly, by observing that when we use a polar representation for the complex scalar field in (1+1)-dimensions described by a theory with Z(N) symmetry, we are naturally led to a SG theory in the phase of this field [6].…”

“…Then using the connection between the SG theory and the 2D neutral CG along with the representation for the relevant soliton creation operators introduced in [7][8][9], and both the Euclidean thermal Green function of the 2D free massless scalar field in coordinate space and its dual [5,10], we obtain our expression for the corresponding solitonic correlation function at finite temperature.…”