Description
Book SynopsisThe notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providing a mathematical construction of models at low dimensions and discussing the removal of the ultraviolet and infrared cut-off, the verification of the axioms and the validity of Ward Identities with the relative anomalies. The second part is devoted to lattice 2D Statistical Physics, analyzing in particular the theory of universality in perturbed Ising models and the computation of the non-universal critical indices in Vertex or Ashkin-Teller models. Finally the third part is devoted to the analysis of complex quantum fluids showing Luttinger of Fermi liquid behavior, like the 1D or 2D Hubbard model.
Table of ContentsRenormalization; Mathematical Techniques; QED2, Thirring and Gross-Neveu Models; Ward Identities; Chiral Anomalies and the Adler-Bardeen Theorem; Vanishing of Beta Function; Wilson Fermion and Axiom Verification; Infrared QED4; Universality in Ising Models; Nonuniversality in Vertex or Askin-Teller Models; The Anisotropic Ashkin-Teller Model; Luttinger Liquids and Spin Chains; The 1D Hubbard Model; Fermi Liquid Behavior in the 2D Hubbard Model; The BCS Model.
