The Form Factors and Quantum Equation of Motion in the sine-Gordon Model

TL;DR

This paper derives exact form factors for operators in the quantum sine-Gordon model using the form factor program, establishing relations between parameters and confirming results with Feynman expansions.

Contribution

It provides a general integral formula for form factors of various operators in the sine-Gordon model, including charge-less operators and the energy-momentum tensor.

Findings

Exact form factors are obtained for multiple operators.

A relation between bare and normalized mass is established.

Results agree with Feynman graph expansion.

Abstract

Using the methods of the 'form factor program' exact expressions of all matrix elements are obtained for several operators of the quantum sine-Gordon model alias the massive Thirring model. A general formula is presented which provides form factors in terms of an integral representation. In particular charge-less operators as for example the current of the topological charge, the energy momentum tensor and all higher currents are considered. In the breather sector it is found the quantum sine-Gordon field equation holds with an exact relation between the 'bare' mass and the normalized mass. Also a relation for the trace of the energy momentum is obtained. All results are compared with Feynman graph expansion and full agreement is found.