Angular Quantization of the Sine-Gordon Model at the Free Fermion Point

TL;DR

This paper applies angular quantization to the Sine-Gordon model at the free fermion point, connecting it with algebraic structures and canonical quantization of free fermions, advancing understanding of integrable quantum field theories.

Contribution

It demonstrates the application of angular quantization to the Sine-Gordon model at the free fermion point and links it with algebraic and canonical quantization frameworks.

Findings

Identifies angular quantization with a representation of an infinite-dimensional algebra.

Constructs Sine-Gordon theory ingredients via algebraic representation theory.

Connects the method with the canonical quantization of free massive Dirac fermions.

Abstract

The goal of this paper is to analyse the method of angular quantization for the Sine-Gordon model at the free fermion point, which is one of the most investigated models of the two-dimensional integrable field theories. The angular quantization method (see hep-th/9707091) is a continuous analog of the Baxter's corner transfer matrix method. Investigating the canonical quantization of the free massive Dirac fermions in one Rindler wedge we identify this quantization with a representation of the infinite-dimensional algebra introduced in the paper q-alg/9702002 and specialized to the free fermion point. We construct further the main ingredients of the SG theory in terms of the representation theory of this algebra following the approach by M.Jimbo, T.Miwa et al.