Quantum Field Theory for Mathematicians

This should be a useful reference for anybody with an interest in quantum theory.

Robin Ticciati (Author)

9780521060257, Cambridge University Press

Paperback / softback, published 4 February 2008

716 pages
23.5 x 15.5 x 3.5 cm, 0.997 kg

"...a very solid pedagogical textbook expounding quantum field theory, as applied to relativistic particle physics...a careful and comprehensive introduction to the physics of the Standard Model together with the mathematical background required to understand it." Siam Review

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.

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.

Subject Areas: Applied mathematics [PBW]