Mathematical Aspects of Quantum Field Theory

This book presents some of the basic ideas and tools of quantum field theory to a mathematical audience.

Edson de Faria (Author), Welington de Melo (Author)

9780521115773, Cambridge University Press

Hardback, published 12 August 2010

314 pages, 10 b/w illus. 45 exercises
23.5 x 15.8 x 2 cm, 0.56 kg

'… a brief, but careful, reasonably balanced, and representative introduction for mathematicians to QFT as it is used in physics.' The Mathematical Intelligencer

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.

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.

Subject Areas: Mathematical physics [PHU], Quantum physics [quantum mechanics & quantum field theory PHQ], Probability & statistics [PBT], Groups & group theory [PBG]