Conformal covariance in the framework of Wilson's renormalization group approach

Abstract

The author constructs a conformal operator in analogy to the generating operator of Wilson's incomplete-integration renormalization group. The invariance of the partition function with respect to that conformal operation yields identities among the cumulants. Evaluating these identities he finds a generalized and corrected form of the selection rule which determines those two-point cumulants which show a long-range tail. A general equation which governs the asymptotic form of the three-point cumulants is established. It is solved for several examples which involve operators of vector- or tensor-type. It is found that surface effects cannot be excluded a priori. However, the asymptotic expressions for the cumulants are consistent with a neglect of surface effects.