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Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory
Edited by: Alan Carey, Australian National University, Canberra, Australia
A publication of the European Mathematical Society.
cover
ESI Lectures in Mathematics and Physics
2011; 280 pp; softcover
Volume: 8
ISBN-10: 3-03719-008-6
ISBN-13: 978-3-03719-008-1
List Price: US$78
Member Price: US$62.40
Order Code: EMSESILEC/8
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This collection of expository articles grew out of the workshop "Number Theory and Physics" held in March 2009 at The Erwin Schrödinger International Institute for Mathematical Physics, Vienna. The common theme of the articles is the influence of ideas from noncommutative geometry (NCG) on subjects ranging from number theory to Lie algebras, index theory, and mathematical physics.

Matilde Marcolli's article gives a survey of relevant aspects of NCG in number theory, building on an introduction to motives for beginners by Jorge Plazas and Sujatha Ramdorai. A mildly unconventional view of index theory, from the viewpoint of NCG, is described in the article by Alan Carey, John Phillips, and Adam Rennie. As developed by Alain Connes and Dirk Kreimer, NCG also provides insight into novel algebraic structures underlying many analytic aspects of quantum field theory. Dominique Manchon's article on pre-Lie algebras fits into this developing research area. This interplay of algebraic and analytic techniques also appears in the articles by Christoph Bergbauer, who introduces renormalization theory and Feynman diagram methods, and Sylvie Paycha, who focuses on relations between renormalization and zeta function techniques.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in number theory and physics.

Table of Contents

  • C. Bergbauer -- Notes on Feynman integrals and renormalization
  • S. Ramdorai, J. Plazas, and M. Marcolli -- Introduction to motives. With an appendix by Matilde Marcolli
  • D. Manchon -- A short survey on pre-Lie algebras
  • S. Paycha -- Divergent multiple sums and integrals with constraints: A comparative study
  • A. Carey, J. Phillips, and A. Rennie -- Spectral triples: Examples and index theory
  • List of contributors
  • Index
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