Noncommutative Geometry and the Standard Model of Elementary Particle Physics

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