QUASI-EXACT SOLVABILITY IN LOCAL FIELD THEORY

Abstract

The quantum mechanical concept of quasi-exact solvability is based on the idea of partial algebraizability of spectral problem. This concept cannot be used directly on the systems with infinte number of degrees of freedom. For such systems a new concept based on the partial Bethe ansatz solvability is proposed. In this letter 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.