Quantization of Solitons and the Restricted Sine-Gordon Model

TL;DR

This paper develops a method to compute form factors in the restricted sine-Gordon model by quantizing solitons, introducing quantum separated variables, and analyzing the model's semi-classical limit and hermitian structure.

Contribution

It introduces a novel quantization approach for solitons in the restricted sine-Gordon model, linking it to an analytical continuation of sine-Gordon and KdV models.

Findings

Explicit soliton wave functions derived.

Connection between restriction and hermitian structure explained.

Semi-classical analysis reveals the model as an analytical continuation.

Abstract

We show how to compute form factors, matrix elements of local fields, in the restricted sine-Gordon model, at the reflectionless points, by quantizing solitons. We introduce (quantum) separated variables in which the Hamiltonians are expressed in terms of (quantum) tau-functions. We explicitly describe the soliton wave functions, and we explain how the restriction is related to an unusual hermitian structure. We also present a semi-classical analysis which enlightens the fact that the restricted sine-Gordon model corresponds to an analytical continuation of the sine-Gordon model, intermediate between sine-Gordon and KdV.