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Noncommutative Geometry and Basic Physics

  • Daniel Kastler
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 543)

Abstract

Alain Connes’ noncommutative geometry, started in 1982 [0], widely develo- ped in 1994 as expounded in his book at this date [0] (it has grown meanwhile) is a systematic quantization of mathematics parallel to the quantization of physics effected in the twenties.This theory widens the scope of mathematics in a manner congenial to physics, reorganizes the existing (“classical”) mathematics of which it produces an hitherto unsuspected unification, and provides basic physics (the synthesis of elementary particles and gravitation) with a programme of renewal which has thus far achieved a clarification of the classical (tree-level) aspects of a new synthesis of the (Euclidean) standard model with gravitation [32],[33]: this is the subject of the present lectures— with the inherent tentative prediction of the Higgs mass.

Keywords

Gauge Group Hopf Algebra Dirac Operator Dual Pair Noncommutative Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Daniel Kastler
    • 1
  1. 1.Centre de Physique ThéoriqueCNRS— LuminyMARSEILLE CEDEX 09FRANCE

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