Exact asymptotic behaviour of fermion correlation functions in the massive Thirring model

Abstract

Abstract. We obtain an exact asymptotic expression for the two-point fermion correlation functions in the massive Thirring model (MTM) and show that, for β 2 = 8π, they reproduce the exactly known corresponding functions of the massless theory, explicitly confirming the irrelevance of the mass term at this point. This result is obtained by using the Coulomb gas representation of the fermionic MTM correlators in the bipolar coordinate system.

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

“…Let us finally remark that in the T → 0 limit the above correlators reduce to the corresponding functions of the zero temperature theory [12]. Also, observe that in the limit α → 0 we recover the thermal fermion correlators of the massless Thirring model.…”

“…Following the above considerations and the same procedure employed at T = 0 [12], we can write the four components of the two-point fermion correlation function of the MTM at finite temperature as…”

“…Comparing (11) with (12) we can see that the only effect of a finite temperature is to exchange the complex variable z for ζ(z). Since ζ(z) is analytic, we conclude that the thermal Green function is obtained from the one at zero temperature by the following conformal mapping [11]: the infinite strip 0 < τ < β and −∞ < x < ∞ is mapped into the region within the upper-half-ζ-plane.…”

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.…”