Mathematical Aspects of Quantum Field Theory
Mathematical Aspects of Quantum Field Theory
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.
- Quantum field theory finally made accessible to mathematicians
- A useful introduction for researchers in mathematics and mathematical physics
- Provides both the mathematical tools and the necessary physical background, giving a more complete picture of the subjects
Reviews & endorsements
'… a brief, but careful, reasonably balanced, and representative introduction for mathematicians to QFT as it is used in physics.' The Mathematical Intelligencer
Product details
No date availableAdobe eBook Reader
9780511910937
0 pages
0kg
10 b/w illus. 45 exercises
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.
