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

Towards the Mathematics of Quantum Field Theory

Authors: Paugam, Frederic

  • Introduces new concepts
  • Provides a clear overview
  • Gives a complete mathematical toolbox for the coordinate-free treatment of classical and quantum field theories
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Hardcover $129.00
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  • Due: October 7, 2016
  • ISBN 978-3-319-37485-7
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About this book

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 to general 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.

About the authors

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.

Reviews

“The book under review is a valuable witness to a wide range of recent developments that aim at unraveling the mathematics of quantum field theory. … the book is well written with an original organization of the material. Its reductionist viewpoint makes it a valuable textbook, especially for the more experienced practitioners in this domain of mathematical physics.” (Walter D. van Suijlekom, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 117, 2015)

“This is a highly specialized monograph exposing current research in a systematic way, aimed at researchers and graduate students in this area. The author has tried to include several examples to illustrate the general methods being treated and ease the reader through the journey.” (Felipe Zaldivar, MAA Reviews, July, 2014)

“This is a complete guide to the mathematics underlying the laws of physics in general and quantum physics in particular. … Frederic Paugam has given us a work of enormous scope and shows students a road to a coordinate-free presentation of mathematical objects underlying classical and quantum field theories. … The book will be useful to graduate student, but also to pure and applied mathematicians interested in modern mathematical developments related to quantum theory.” (Gert Roepstorff, zbMATH, Vol. 1287, 2014)

Table of contents (24 chapters)

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-04564-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-04563-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 7, 2016
  • ISBN 978-3-319-37485-7
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Towards the Mathematics of Quantum Field Theory
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
59
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-04564-1
DOI
10.1007/978-3-319-04564-1
Hardcover ISBN
978-3-319-04563-4
Softcover ISBN
978-3-319-37485-7
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XVI, 487
Number of Illustrations and Tables
76 b/w illustrations, 1 illustrations in colour
Topics