Renormalization : an introduction
Author(s)
Bibliographic Information
Renormalization : an introduction
（Texts and monographs in physics）
Springer, c1999
Corrected 2nd printing
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Note
Includes bibliographical references (p. [229]-230) and index
Description and Table of Contents
Description
This monograph is the first to present the recently discovered renormalization techniques for the Schroedinger and Dirac equations, providing a mathematically rigorous, yet simple and clear introduction to the subject. It develops field-theoretic techniques such as Feynman graph expansions and renormalization, taking pains to make all proofs as simple as possible by using generating function techniques throughout. Renormalization is performed by using an exact renormalization group differential equation, a technique that provides simple but complete proofs of the theorems.
Table of Contents
- 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.
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