Equivalent bosonic theory for the massive Thirring model with non-local interaction

TL;DR

This paper extends the massive Thirring model to include non-local interactions and demonstrates its equivalence to a non-local sine-Gordon theory, generalizing Coleman's correspondence and suggesting applications in condensed matter and quantum field theories.

Contribution

It introduces a non-local extension of the massive Thirring model and proves its equivalence to a non-local sine-Gordon theory, generalizing Coleman's equivalence.

Findings

Established the non-local equivalence between the extended Thirring and sine-Gordon models.

Provided a framework for analyzing non-local interactions in 1D quantum systems.

Discussed potential applications in strongly correlated systems and finite-size quantum theories.

Abstract

We study, through path-integral methods, an extension of the massive Thirring model in which the interaction between currents is non-local. By examining the mass-expansion of the partition function we show that this non-local massive Thirring model is equivalent to a certain non-local extension of the sine-Gordon theory. Thus, we establish a non-local generalization of the famous Coleman's equivalence. We also discuss some possible applications of this result in the context of one-dimensional strongly correlated systems and finite-size Quantum Field Theories.