Manfred Salmhofer

Renormalization (eBook, PDF)

An Introduction

• Format: PDF

Produktbeschreibung

This book provides a simple, but mathematically rigorous, introduction to perturbative renormalization. It can be read by students from the third year on and will leads them to a level where they can start reading the current research literature. The book gives a thorough introduction to the field-theoretic techniques required for renormalization. Special effort has been devoted to simplifying combinatorial proofs as much as possible by using generating function techniques. A renormalization group differential equation is used to study the flow of Wilson's effective action. This differential equation technique, developed during the last few years, is used to give simple but complete proofs of renormalizability theorems. The book contains an introduction to renormalization in models of solid-state physics.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 231
• Erscheinungstermin: 14. März 2013
• Englisch
• ISBN-13: 9783662038734
• Artikelnr.: 53317561

Inhaltsangabe

1. Field Theory.- 2. Techniques.- 3. The Renormalization Group.- 4. The Fermi Surface Problem.- A. Appendix to Chapters 1-3.- A.1 A Topology on the Ring of Formal Power Series.- A.2 Fourier Transformation.- A.3 Properties of the Boson Propagator.- A.4 Wick Reordering for Bosons.- A.5 The Lower Bound for the Sunset Graph.- B. Appendix to Chapter 4.- B.1 Fermionic Fock Space.- B.2 Calculus on Grassmann Algebras.- B.3 Grassmann Gaussian Integrals.- B.4 Gram's Inequality; Bounds for Gaussian Integrals.- B.5 Grassmann Integrals for Fock Space Traces.- B.5.1 Delta Functions and Integral Kernels.- B.5.2 The Formula for the Trace.- B.5.3 The Time Continuum Limit.- B.5.4 Nambu Formalism.- B.5.5 Matsubara Frequencies.- B.6 Feynman Graph Expansions.- B.7 The Thermodynamic Limit in Perturbation Theory.- B.8 Volume Improvement Bounds.- B.8.1 The One-Loop Volume Bound.- B.8.2 The Two-Loop Volume Bound.- References.

Rezensionen

From the reviews "In summary, this is an excellent reference text for anyone interested in the mathematical formulation of renormalization and quantum field theory and should be seriously considered as an addition to a professional or university library." (A.G. Williams, The Physicist, 1999) "This book concentrates very much on the technical matters one has to be aware of in order to perform an actual calculation, and explains all elementary steps of the method. In spite of that, the author also finds the opportunity to clarify the physical situation behind. He also points out the similarities and connections that exist between different branches of theoretical physics like statistical mechanics of polymers, critical phenomena, and field theories, where renormalization methods are usually applied." (M. Benedict, Acta Scientiarum Mathematicarum, 2000)