Mathematical Aspects of Quantum Field Theory

Erscheinungsjahr 2016
ISBN: 978-0-521-11577-3
Verlag: Cambridge University Press

Buch, Englisch, Band 127, 320 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 662 g

Reihe: Cambridge Studies in Advanced Mathematics

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.
• 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

Autoren/Hrsg.

De Faria, Edson

De Melo, Welington

Fachgebiete

• Naturwissenschaften Physik Quantenphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

De Melo, Welington
Welington de Melo is a Professor in the Instituto de Matemática Pura e Aplicada in Rio de Janeiro.

De Faria, Edson
Edson de Faria is a Professor in the Instituto de Matemática e Estatística at the Universidade de São Paulo.