Scaling of nonlocal operators.

Abstract

An exact scaling relation developed for nonlocal operators is presented. The matrix elements of a general nonlocal operator are related to a set of reduced matrix elements through scaling coefficients which do not explicitly depend on the particular nonlocal operator. The theory reduces to a conventional local scaling formulation in that limit. The guide to developing the nonlocal scaling relation comes from consideration of general symmetry properties of the nonlocal operator in a chosen representation. Operators with high degrees of symmetry will generally lead to scaling relations requiring a small number of scaling coefficients for practical applications. The theory is expected to be useful not only for providing exact nonlocal scaling relations but also as a tool for developing approximate scaling relations which still retain the nonlocal nature of the operator to an appropriate extent.