Particle-Field Duality and Form Factors from Vertex Operators

TL;DR

This paper introduces a duality-based method to compute form factors directly in the field space using vertex operators, with explicit constructions and bosonization, applied to the sine-Gordon model.

Contribution

It presents a novel approach to calculate form factors via vertex operators in the field space, extending previous work and including the periodic sector.

Findings

Explicit construction of vertex operators in radial quantization

Bosonization of vertex operators in momentum space

Computed form factors in the sine-Gordon model

Abstract

Using a duality between the space of particles and the space of fields, we show how one can compute form factors directly in the space of fields. This introduces the notion of vertex operators, and form factors are vacuum expectation values of such vertex operators in the space of fields. The vertex operators can be constructed explicitly in radial quantization. Furthermore, these vertex operators can be exactly bosonized in momentum space. We develop these ideas by studying the free-fermion point of the sine-Gordon theory, and use this scheme to compute some form-factors of some non-free fields in the sine-Gordon theory. This work further clarifies earlier work of one of the authors, and extends it to include the periodic sector.