Quantum Field Theory for Mathematicians (Encyclopedia of Mathematics and its Applications, Series Number 72)

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. 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. "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." "This book 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."--BOOK JACKET.

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