Towards complex(rational) powers of free fields, generalized $\beta\gamma$ systems and non-polynomial quantum field theory

TL;DR

This paper extends the $eta\gamma$ system by introducing complex and rational powers of fields, developing methods to compute Green functions, and exploring potential applications in non-polynomial quantum field theories.

Contribution

It introduces two novel approaches for computing Green functions in generalized $eta\gamma$ systems with complex powers, expanding the theoretical framework and computational tools.

Findings

Defined complex powers via integral representation enabling computation of conformal blocks

Developed recursion equations for Green functions and found multiple solutions

Discussed potential applications in non-polynomial quantum field theories

Abstract

The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed. First the complex(rational) powers are defined via an integral representation,that allows 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 is found. A lot of possible applications is briefly discussed.