Constructive Physics

Addressing graduate students and researchers in physics and mathematics, this volume fills a gap in the literature. It is an instructive introduction to modern contructive physics, field theory and statistical mechanics, and a survey on the most recent research in this field.

Some questions for constructive field theorists.- Trees, forests and jungles: A botanical garden for cluster expansions.- Weak perturbations of the massless Gaussian measure.- On renormalization group flows and polymer algebras.- Renormalizing partial differential equations.- Supersymmetric quantum field theory.- Equivalence of the Euclidean and Wightman field theories.- Construction of the gross-neveu model in dimension 3.- Mass generation in a one-dimensional fermi model.- Mass generation in the large N Gross-Neveu model.- U(1) gauge theory on a torus.- A low temperature expansion and "spin wave picture" for classical N-vector models.- Renormalization group approach to zero temperature bose condensation.- Random and interacting surfaces.- Fermi liquids in two-space dimensions.- The self-avoiding walk in four dimensions.- Charge correlations for the two-dimensional Coulomb gas.- Weakly self-avoiding polymers in four dimensions.