COVARIANT DERIVATIVES AND THE RENORMALIZATION-GROUP EQUATION

The renormalization group equation for N-point correlation functions c an be interpreted in a geometrical manner as an equation for Lie trans port of amplitudes in the space of couplings. The vector held generati ng the diffeomorphism has components given by the beta functions of th e theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated bec omes close to any other. This modification necessitates the introducti on of a connection on the space of couplings and new terms appear in t he renormalization group equation involving covariant derivatives of t he beta function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansi on coefficients, but there remains an arbitrariness in its definition.