Exact form factors in integrable quantum field theories: the sine-Gordon model (II)

TL;DR

This paper develops a model-independent integral approach to compute exact form factors in the sine-Gordon quantum field theory, confirming results with Feynman expansions and exploring bound states and conserved charges.

Contribution

It introduces an off-shell Bethe Ansatz method for form factors, applies it to the sine-Gordon model, and derives explicit formulas for bound states and conserved charges.

Findings

Exact form factors for local operators are obtained.

The approach confirms classical conserved charge eigenvalues.

Explicit formulas for lowest breather form factors are derived.

Abstract

A general model independent approach using the `off-shell Bethe Ansatz' is presented to obtain an integral representation of generalized form factors. The general techniques are applied to the quantum sine-Gordon model alias the massive Thirring model. Exact expressions of all matrix elements are obtained for several local operators. In particular soliton form factors of charge-less operators as for example all higher currents are investigated. It turns out that the various local operators correspond to specific scalar functions called p-functions. The identification of the local operators is performed. In particular the exact results are checked with Feynman graph expansion and full agreement is found. Furthermore all eigenvalues of the infinitely many conserved charges are calculated and the results agree with what is expected from the classical case. Within the frame work of integrable quantum field theories a general model independent `crossing' formula is derived. Furthermore the `bound state intertwiners' are introduced and the bound state form factors are investigated. The general results are again applied to the sine-Gordon model. The integrations are performed and in particular for the lowest breathers a simple formula for generalized form factors is obtained.