The "Bootstrap Program" for Integrable Quantum Field Theories in 1+1 Dim

TL;DR

This paper reviews the bootstrap program for constructing integrable quantum field theories in 1+1 dimensions, illustrating it with the sine-Gordon model and proposing general formulas for form factors and conserved charges.

Contribution

It introduces a comprehensive bootstrap approach for integrable QFTs, including new formulas for form factors and conserved charge eigenvalues using the off-shell Bethe Ansatz.

Findings

Proposed general formulas for form factors in integrable models

Calculated eigenvalues of higher conserved charges

Derived quantum operator equations and renormalization constants

Abstract

The purpose of the "bootstrap program" is to construct integrable quantum field theories in 1+1 dimensions in terms of their Wightman functions explicitly. As an input the integrability and general assumptions of local quantum field theories are used. The object is to be achieved in tree steps: 1) The S-matrix is obtained using a qualitative knowledge of the particle spectrum and the Yang-Baxter equations. 2) Matrix elements of local operators are calculated by means of the "form factor program" using the S-matrix as an input. 3) The Wightman functions are calculated by taking sums over intermediate states. The first step has been performed for a large number of models and also the second one for several models. The third step is unsolved up to now. Here the program is illustrated in terms of the sine-Gordon model alias the massive Thirring model. Exploiting the "off-shell" Bethe Ansatz we propose general formulae for form factors. For example the n-particle matrix element for all higher currents are given and in particular all eigenvalues of the higher conserved charges are calculated. Furthermore quantum operator equations are obtained in terms of their matrix elements, in particular the quantum sine-Gordon field equation. Exact expressions for the finite wave function and mass renormalization constants are calculated.