Mathematical Aspects of Quantum Field Theory

Edson de Faria, Welington de Melo

• Publisher: Cambridge University Press
• Year: 2010
• Print ISBN:
  9780521115773
• eBook ISBN:
  9780511910937
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

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.

Table of contents

• Cover
• Half-title
• Series-title
• Title
• Copyright
• Contents
• Foreword
• 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