Quasi-Exact Solvability in Local Field Theory. First Steps

TL;DR

This paper introduces a new concept of quasi-exact solvability for quantum field theories, based on partial Bethe Ansatz solvability, and provides a method to construct such models on a one-dimensional lattice.

Contribution

It extends the idea of quasi-exact solvability from quantum mechanics to field theories using a novel approach based on partial Bethe Ansatz.

Findings

Demonstrates constructivity of the new solvability concept

Provides a method for building local, hermitian Hamiltonian models

Applicable to one-dimensional lattice field theories

Abstract

The quantum mechanical concept of quasi-exact solvability is based on the idea of partial algebraizability of spectral problem. This concept is not directly extendable to the systems with infinite number of degrees of freedom. For such systems a new concept based on the partial Bethe Ansatz solvability is proposed. In present paper we demonstrate the constructivity of this concept and formulate a simple method for building quasi-exactly solvable field theoretical models on a one-dimensional lattice. The method automatically leads to local models described by hermitian hamiltonians.