QUASI-EXACT SOLVABILITY IN LOCAL-FIELD THEORY

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 infinite number of degree s of freedom. For such systems a new concept based on the partial Beth e ansatz solvability is proposed. In this letter we demonstrate the co nstructivity of this concept and formulate a simple method for buildin g quasi-exactly solvable field theoretical models on a one-dimensional lattice. The method automatically leads to local models described by Hermitian Hamiltonians.