The Exact Quantum Sine-Gordon Field Equation and Other Non-Perturbative Results

TL;DR

This paper derives exact non-perturbative results for the quantum sine-Gordon model, including matrix elements, field equations, and conserved charges, confirming their consistency with perturbative expansions.

Contribution

It provides the first exact expressions for matrix elements of key operators and establishes the precise relation between bare and renormalized masses in the quantum sine-Gordon model.

Findings

Exact matrix elements for fundamental operators obtained.

Quantum sine-Gordon field equation verified with exact mass relation.

Eigenvalues of all higher conserved charges explicitly solved.

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: all powers of the fundamental bose field, general exponentials of it, the energy momentum tensor and all higher currents. It is found that the quantum sine-Gordon field equation holds with an exact relation between the "bare" mass and the renormalized mass. Also a relation for the trace of the energy momentum is obtained. The eigenvalue problem for all higher conserved charges is solved. All results are compared with Feynman graph expansions and full agreement is found.