Noncommutative Geometry and the Standard Model of Elementary Particle Physics

2002
ISBN: 978-3-540-44071-0
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 596, 350 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1520 g

Reihe: Lecture Notes in Physics

aiming at a more conceptual understanding of classical and qu- tum ?eld theory from a novel mathematical point of view.

Zielgruppe

Research

Autoren/Hrsg.

Scheck, Florian

Upmeier, Harald

Werner, Wend

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik Teilchenphysik
• Naturwissenschaften Physik Quantenphysik Kernphysik
• Mathematik | Informatik Mathematik Geometrie Geometrie der modernen Physik

Inhaltsverzeichnis

Foundations of Noncommutative Geometry and Basic Model Building.- Spectral Triples and Abstract Yang-Mills Functional.- Real Spectral Triples and Charge Conjugation.- The Commutative Case: Spinors, Dirac Operator and de Rham Algebra.- Connes’ Trace Formula and Dirac Realization of Maxwell and Yang-Mills Action.- The Einstein-Hilbert Action as a Spectral Action.- Spectral Action and the Connes-Chamsedinne Model.- The Lagrangian of the Standard Model Derived from Noncommutative Geometry.- Dirac Operator and Real Structure on Euclidean and Minkowski Spacetime.- The Electro-weak Model.- The Full Standard Model.- Standard Model Coupled with Gravity.- The Higgs Mechanism and Spontaneous Symmetry Breaking.- New Directions in Noncommutative Geometry and Mathematical Physics.- The Impact of NC Geometry in Particle Physics.- The su(2 1) Model of Electroweak Interactions and Its Connection to NC Geometry.- Quantum Fields and Noncommutative Spacetime.- NC Geometry and Quantum Fields: Simple Examples.- Dirac Eigenvalues as Dynamical Variables.- Hopf Algebras in Renormalization and NC Geometry.- NC Geometry of Strings and Duality Symmetry.