THE O(N) SIGMA-MODEL LAPLACIAN

For fields that vary slowly on the scale of the lightest mass the loga rithm of the vacuum functional of a massive quantum field theory can b e expanded in terms of local functionals satisfying a form of the Schr odinger equation, the principal ingredient of which is a regulated fun ctional Laplacian. We construct to leading order a Laplacian for the O (N) sigma-model that acts on such local functionals. It is determined by imposing rotational invariance in the internal space together with closure of the Poincare algebra.