A Renormalization Group Method by Harmonic Extensions and the Classical Dipole Gas

摘要: In this paper, we develop a new renormalization group method, which is based on conditional expectations and harmonic extensions, to study functional integrals of small perturbations Gaussian fields. one integrates fields inside domains at all scales conditioning the outside these domains, by variation principle solves local elliptic problems. It does not rely an priori decomposition covariance. We apply method model classical dipole gas lattice, show that scaling limit generating function with smooth test functions renormalized free field.