Noncommutative geometry and physics: renormalisation, motives, index theory
by Carey, Alan
This collection of expository articles grew out of the workshop "Number Theory and Physics" held in March 2009 at the 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 introduct…
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- Full title :Noncommutative geometry and physics : renormalisation, motives, index theory / Alan Carey ... [et al.], ed.
Summary
This collection of expository articles grew out of the workshop "Number Theory and Physics" held in March 2009 at the 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 renormalisation theory and Feynman diagram methods, and Sylvie Paycha, who focuses on relations between renormalisation and zetafunction techniques.
Read More ↓Edition Statements
- Publication Date:2011.
Publication Statements
- Publisher(s):European Mathematical Society
- Place of Publication:Zürich
- Language:eng
- Publication Date:2011.
Notes
In European Mathematical Society (Blitz-Mels, mai 2011).
Versement en lot.
The Physical Object
- Description:1 texte électronique : : fichier PDF.
Edition Identifiers
- ISBN:3037190086, 9783037190081
- oclc:ocn747914318
- LC Classification:QC20.7.D52
- Dewey Decimal:516.36
Table of Contents
Notes on Feynman integrals and renormalization / Christoph Bergbauer -- Introduction to motives: with an appendix by Matilde Marcolli / Sujatha Ramdorai, Jorge Plazas, and Matilde Marcolli -- A short survey on pre-Lie algebras / Dominique Manchon -- Divergent multiple sums and integrals with constraints: a comparative study / Sylvie Paycha -- Spectral triples: examplesand index theory / Alan Carey, John Phillips, and Adam Renni.
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