Sine-Gordon breather form factors and quantum field equations

TL;DR

This paper derives exact form factors for sine-Gordon breather states, confirms the quantum field equation, and relates bare and renormalized masses, providing a comprehensive non-perturbative analysis.

Contribution

It provides explicit formulas for breather form factors of various operators and proves the quantum sine-Gordon field equation and mass relations.

Findings

Exact breather form factors for multiple operators derived.

Quantum sine-Gordon field equation confirmed.

Mass renormalization relation established.

Abstract

Using the results of previous investigations on sine-Gordon form factors exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental bose field, general exponentials of it, the energy momentum tensor and all higher currents. Formulae for the asymptotic behavior of bosonic form factors are presented which are motivated by Weinberg's power counting theorem in perturbation theory. It is found that the quantum sine-Gordon field equation holds and an exact relation between the ``bare'' mass and the renormalized mass is obtained. Also a quantum version of a classical relation for the trace of the energy momentum is proven. The eigenvalue problem for all higher conserved charges is solved. All results are compared with perturbative Feynman graph expansions and full agreement is found.