Towards the Mathematics of Quantum Field Theory

2014
ISBN: 978-3-319-04563-4
Verlag: Springer International Publishing

Buch, Englisch, Band 59, 487 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 8749 g

Reihe: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature.
The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications togeneral gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.

Zielgruppe

Research

Autoren/Hrsg.

Paugam, Frédéric

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Geometrie der modernen Physik
• Naturwissenschaften Physik Quantenphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Introduction.- Mathematical Preliminaries.- Classical Trajectories and Fields.- Quantum Trajectories and Fields.- Appendices.

Über Autor(innen)

Frédéric Paugam is a pure mathematician working at the University Pierre et Marie Curie. He started his career in arithmetic geometry, working on Galois representations and abelian varieties. He first became interested in the mathematics of quantum physics through the study of quantum statistical mechanics. He then approached quantum field theory with the categorical methods that he had learned from the work of Grothendieck’s school. He has since held various courses on this subject, allowing him to develop the tools and content of this book with the aim of teaching in mind.