Operator product constants in the 2-dimensional conformal field theories

Abstract

All the operator product constants (fusion coefficients) in the minimal unitary conformal quantum field theories are obtained in closed formula using only second-order Fuchsian-type differential equations with the help of monodromy invariances and crossing symmetries of 4-point correlation functions. We have demonstrated that all fusion coefficients can be determined if we follow certain well-defined path. The explicit results are given by mathematical induction in chapter 4.