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Title................: Non-Perturbative Renormalization
Type.................: Ebook
Reader...............: PDF Reader
Size.................: 1.68 MB
Torrent Hash.........: A015D499 9729CBB8 82C74660 7A500774 F9766D87
Posted by............: ~tqw~


Non Perturbative Renormalization~tqw~_darksiderg preview 0
The 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 Contents:
Introduction to Renormalization 1
1 Basic Notions 3
2 Fermionic Functional Integrals 27
3 The Ultraviolet Problem in Massive QED2 59
4 Infrared Problem and Anomalous Behavior 81
5 Ward Identities and Vanishing of the Beta Function 105
6 Thirring and Gross-Neveu Models 125
7 Axioms Verification and Wilson Fermions 133
8 Infraed QED4 with Large Photon Mass 143
Lattice Statistical Mechanics 147
9 Universality in Generalized Ising Models 149
10 Nonuniversality in Vertex or Isotropic Ashkin-Teller Models 165
11 Universality-Nonuniversality Crossover in the Ashkin-Teller Model 181
Quantum Liquids 199
12 Spinless Luttinger Liquids 201
13 The 1d Hubbard Model 225
14 Fermi Liquids in Two Dimensions 239
15 BCS Model with Long Range Interaction 263
Appendix A The Ising Model Fermionic Representation 273
A.1 The Grassmann representation of the 2d Ising model with open boundary
conditions 273
A.2 The Grassmann representation of the 2d Ising model with periodic boundary
conditions 283
Bibliography 287

Product Details:
* ISBN: 9812792392
* ISBN-13: 9789812792396
* Format: Hardcover, 300pp
* Publisher: World Scientific Publishing Company, Incorporated
* Pub. Date: April 2008

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