Mathematical Aspects of Quantum Field Theory

by Edson de Faria, Welington de Melo

Overview

Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

Product Details

ISBN-13:	9781139635523
Publisher:	Cambridge University Press
Publication date:	08/12/2010
Series:	Cambridge Studies in Advanced Mathematics , #127
Sold by:	Barnes & Noble
Format:	eBook
File size:	14 MB
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About the Author

Edson de Faria is a Professor in the Instituto de Matemática e Estatística at the Universidade de São Paulo.
Welington de Melo is a Professor in the Instituto de Matemática Pura e Aplicada in Rio de Janeiro.

Table of Contents

Foreword Dennis Sullivan; Preface; 1. Classical mechanics; 2. Quantum mechanics; 3. Relativity, the Lorentz group and Dirac's equation; 4. Fiber bundles, connections and representations; 5. Classical field theory; 6. Quantization of classical fields; 7. Perturbative quantum field theory; 8. Renormalization; 9. The standard model; Appendix A. Hilbert spaces and operators; Appendix B. C* algebras and spectral theory; Bibliography; Index.