Frédéric Paugam

eBook, PDF

Towards the Mathematics of Quantum Field Theory (eBook, PDF)

Beschreibung

The aim of this book is to introduce mathematicians (and, in particular, graduate students) to the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in play. This should in turn promote interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, even if the mathematical one is 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 to generalgauge 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. The book is primarily intended for pure mathematicians (and in particular graduate students) who would like to learn about the mathematics of quantum field theory.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 3.79MB

Autor

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.

Produktdetails

• Verlag: Springer Nature Switzerland
• Seitenzahl: 487
• Erscheinungstermin: 20. Februar 2014
• Englisch
• ISBN-13: 9783319045641
• Artikelnr.: 43787530