TOWARDS COMPLEX (RATIONAL) POWERS OF FREE FIELDS, GENERALIZED BETA-GAMMA SYSTEMS AND NONPOLYNOMIAL QUANTUM-FIELD THEORY

The beta gamma system is generalized by complex (rational) powers of the fields, which leads to a corresponding extension of the Fock space. Two different approaches to computing the Green functions of the physical operators are proposed. First, the complex (rational) powers are defined via an integral representation, which allows one to compute the conformal blocks, Green functions and structure constants of OPA. Next, an approach based on a system of recursion equations for the Green functions is developed. A number of solutions of the system are found. As a result, a new class of 2D quantum field theories is constructed.