Quantum Field Theory for Mathematicians

ISBN-13: 9780521632652 / Angielski / Twarda / 1999 / 716 str.

Robin Ticciati; R. Ticciati; G. -C Rota

Opis

Ticciati's approach to quantum field theory falls between building a mathematical model of the subject and presenting the mathematics that physicists actually use. It begins 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: canonical quantization of scalar fields, Weyl, Dirac and vector fields, functional integral quantization, the standard model of the electroweak and strong interactions, renormalization. This should be a useful reference for those interested in quantum theory and related areas of function theory, functional analysis, differential geometry or topological invariant theory.

Recenzje

"...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

Spis treści

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.