Towards the Mathematics of Quantum Field Theory

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.

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

"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)