Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory

ISBN-10: 3037190086
ISBN-13: 9783037190081
Category: Geometry, Algebraic
Pages: 288
Language: English
Published: 2011
Publisher: European Mathematical Society
Author: Alan L. Carey

Description

This collection of expository articles grew out of the workshop ``Number Theory and Physics'' held in March 2009 at The Erwin Schrodinger 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.

Get the book

Other editions

Noncommutative Geometry and Physics: Proceedings of the COE International Workshop,...
- 2005
- 378 pages
- Paperback
- World Scientific Publishing Company Incorporated

Similar books

Algebraic Geometry: Salt Lake City 2015 : 2015 Summer Research Institute, July 13-31, 2015, University of Utah, Salt Lake City,...
By Richard Thomas
This work was partially supported by NSF grant 1262531 and a Royal Society Wolfson Research Merit Award. c2018 Mark Gross and Bernd Siebert 1More common seems to be the usage of characteristic, but 199 Proceedings of Symposia in Pure ...
String-Math 2015
By Si Li
This volume contains the proceedings of the conference String-Math 2015, which was held from December 31, 2015-January 4, 2016, at Tsinghua Sanya International Mathematics Forum in Sanya, China.
A Survey of the Hodge Conjecture
By James Dominic Lewis
This comprehensive approach to the book gives it a 'user-friendly' style. Readers need not search elsewhere for various results. The book is suitable for use as a text for a topics course in algebraic geometry.
Algebraic Statistics
By Seth Sullivant
Richard M. Karp, Reducibility among combinatorial problems, Complexity of computer computations (Proc. ... MR779900 Daphne Koller and Nir Friedman, Probabilistic graphical models: Principles and techniques, Adaptive Computation and ...
Applications of Computational Algebraic Geometry: American Mathematical Society Short Course, January 6-7, 1997, San Diego, California
By David A. Cox, Dinesh N. Manocha
... Dinesh N. Manocha, Xenia H. Kramer, Reinhard C. Laubenbacher, Rekha R. Thomas, John B. Little David A Cox, PH. ... [Laz2] |Lit] [Man1] References W. Adams and P. Loustaunau, Introduction to Gröbner Bases, AMS, Providence, RI, 1994.
Trigonometry: Student text
By Margaret L. Lial, Charles David Miller
The mast of Gale Stockdale's boat is 32 feet high . If it intercepts an angle of 2 ° 10 ' , how far away is it ? 28. A television tower 530 m high intercepts an angle of 2 ° 40 ' . How far away is the tower ? : Find the areas of each of ...
Introduction to Hodge Theory
By José Bertin
This book consists of expositions of aspects of modern Hodge theory, with the purpose of providing the nonexpert reader with a clear idea of the current state of the subject.
Real Algebraic Geometry and Ordered Structures: AMS Special Session on Real Algebraic Geometry and Ordered Algebraic Structures Held at Louisiana...
By Charles N. Delzell, James J. Madden
Examples of Robinson. In the late 1960s at Berkeley, Raphael M. Robinson [77, p. 264 saw “an unpublished example of a ternary sextic worked out recently by W. J. Ellison using Hilbert's method (see $3a). It is, as would be expected, ...
Mathematical Surveys and Monographs

Mathematical Surveys and Monographs
From Hodge Theory to Integrability and TQFT: Tt*-geometry : International Workshop from TQFT to Tt* and Integrability : May 25-29,...
By International Workshop from TQFT to tt* and Integrability
|Raj J.H. Rawnsley, f-structures, f-twistor spaces and harmonic maps, Geometry seminar “Luigi Bianchi” II–1984, 85–159, Lecture Notes in Math., 1164, Springer, Berlin, 1985. [Rel W. Reichel, Uber die Trilinearen Alternierenden Formen in ...