Thirring sine-Gordon relationship by canonical methods

TL;DR

This paper rederives the quantum relationship between the Thirring and sine-Gordon models using canonical methods, providing insights into soliton operators and their algebraic properties.

Contribution

It offers a novel canonical approach to derive the Thirring-sine-Gordon relationship and constructs Mandelstam soliton operators as solutions to Poisson brackets.

Findings

Confirmed the anticommutation relations of soliton operators

Derived the Mandelstam relation via Hamiltonian to Lagrangian transition

Validated the Poisson brackets for composite fermionic operators

Abstract

Using the canonical method developed for anomalous theories, we present the independent rederivation of the quantum relationship between the massive Thirring and the sine-Gordon models. The same method offers the possibility to obtain the Mandelstam soliton operators as a solution of Poisson brackets "equation" for the fermionic fields. We checked the anticommutation and basic Poisson brackets relations for these composite operators. The transition from the Hamiltonian to the corresponding Lagrangian variables produces the known Mandelstam's result.