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

Abstract

We show that the quantum solitons occurring in theories describing a complex scalar field in (1 + 1)-dimensions with a <i>Z</i>(N) symmetry may be identified with sine-Gordon quantum solitons in the phase of this field. Then using both the Euclidean thermal Green function of the two-dimensional free massless scalar field in coordinate space and its dual, we obtain an explicit series expression for the corresponding solitonic correlation function at finite temperature

The Rise of Solitons in Sine-Gordon Field Theory: From Jacobi Amplitude to Gudermannian Function

“…The sine-Gordon field theory and the associated massive Thirring model [1] are some of the best studied quantum field theories. In view of its connections to other important physical models, some of which in principle admit actual realizations in nature [2,3], a huge mass of important exact results have been obtained for this fascinating integrable system [4][5][6][7]. However, no less fascinating are the remarkable mathematical and physical properties of its soliton (or "solitary wave") solutions which have contributed, along the last decades, to turn the physics of solitons into a very active research topic.…”