Quantum field theory for mathematicians
Author(s)
Bibliographic Information
Quantum field theory for mathematicians
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 72）
Cambridge University Press, 2008
- : pbk
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Note
"Digitally printed version (with corrections) 2008"--T.p. verso
Originally published: 1999
Includes bibliographical references (p. [687]-688) and index
"Paperback re-issue"--Back cover
Description and Table of Contents
Description
The approach to quantum field theory in this book is part way between building a mathematical model of the subject and presenting the mathematics that physicists actually use. It starts with the need to combine special relativity and quantum mechanics and culminates in a basic understanding of the standard model of electroweak and strong interactions. The book is divided into five parts: 1. Canonical quantization of scalar fields; 2. Weyl, Dirac and vector fields; 3. Functional integral quantization; 4. The standard model of the electroweak and strong interactions; 5. Renormalization. This should be a useful reference for anybody with interests in quantum theory and related areas of function theory, functional analysis, differential geometry or topological invariant theory.
Table of Contents
- 1. Relativistic quantum mechanics
- 2. Fock space, the scalar field and canonical quantization
- 3. Symmetries, conserved currents and conserved quantities
- 4. The scattering matrix and Feynmann diagrams
- 5. Differential transition probabilities and predictions
- 6. Representations of the Lorentz group
- 7. Two-component scalar fields
- 8. Four-component scalar fields
- 9. Massive vector fields
- 10. Reformulating scattering theory
- 11. Functional integral quantization
- 12. Quantization of gauge theories
- 13. Anomalies of gauge theories
- 14. SU(3) representation theory
- 15. The structure of the standard model
- 16. Hadrons, flavor symmetry and nucleon-pion interactions
- 17. Tree-level applications of the standard model
- 18. Regularization and renormalization
- 19. Renormalization of QED
- 20. Renormalization and preservation of symmetries
- 21. The renormalization group equations.
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