Noncommutative Geometry and the Standard Model of Elementary Particle Physics

Ralf Holtkamp (auth.), Florian Scheck, Harald Upmeier, Wend Werner (eds.)3540440712, 9783540440710

The outcome of a close collaboration between mathematicians and mathematical physicists, these lecture notes present the foundations of A. Connes noncommutative geometry as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.

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Table of contents :
Front Matter….Pages 1-1
Spectral Triples and Abstract Yang-Mills Functional….Pages 4-10
Real Spectral Triples and Charge Conjugation….Pages 11-20
The Commutative Case: Spinors, Dirac Operator and de Rham Algebra….Pages 21-39
Connes’ Trace Formula and Dirac Realization of Maxwell and Yang-Mills Action….Pages 40-74
The Einstein-Hilbert Action as a Spectral Action….Pages 75-108
Spectral Action and the Connes-Chamsedinne Model….Pages 109-132
Front Matter….Pages 134-134
Dirac Operator and Real Structure on Euclidean and Minkowski Spacetime….Pages 136-151
The Electro-weak Model….Pages 152-171
The Full Standard Model….Pages 172-215
Standard Model Coupled with Gravity….Pages 216-229
The Higgs Mechanism and Spontaneous Symmetry Breaking….Pages 230-240
Front Matter….Pages 242-242
The Impact of NC Geometry in Particle Physics….Pages 244-259
The su (2|1) Model of Electroweak Interactions and Its Connection to NC Geometry….Pages 260-270
Quantum Fields and Noncommutative Spacetime….Pages 271-277
NC Geometry and Quantum Fields: Simple Examples….Pages 278-298
Dirac Eigenvalues as Dynamical Variables….Pages 299-312
Hopf Algebras in Renormalization and NC Geometry….Pages 313-324
NC Geometry of Strings and Duality Symmetry….Pages 325-337