Mathematical Aspects of Quantum Field Theory
$69.99 (P)
Part of Cambridge Studies in Advanced Mathematics
- Authors:
- Edson de Faria, Universidade de São Paulo
- Welington de Melo, IMPA, Rio de Janeiro
- Date Published: September 2010
- availability: Available
- format: Hardback
- isbn: 9780521115773
$
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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.
Read more- 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
"The authors do quite a good job of giving a complete, yet concise treatment of this field theory that is crucial in our understanding of the world of particle physics."
Walter D. van Suijlekom, Mathematical ReviewsSee more reviews"… a brief, but careful, reasonably balanced, and representative introduction for mathematicians to QFT as it is used in physics."
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×Product details
- Date Published: September 2010
- format: Hardback
- isbn: 9780521115773
- length: 314 pages
- dimensions: 235 x 158 x 20 mm
- weight: 0.56kg
- contains: 10 b/w illus. 45 exercises
- availability: Available
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.
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