Noncommutative Geometry and the Standard Model of Elementary Particle Physics

ISBN-13: 9783540440710 / Angielski / Twarda / 2002 / 350 str.

F. Scheck; H. Upmeier; Wend Werner

Opis

Aconferenceon NoncommutativeGeometryandtheStandardModelof- ementaryParticlePhysics washeldattheHesselbergAcademy(innorthern Bavaria, Germany) during the week of March 14 19, 1999. The aim of the conference was to give a systematic exposition of the mathematical foun- tions and physical applications of noncommutative geometry, along the lines developedbyAlainConnes. Theconferencewasactuallypartofacontinuing series of conferences at the Hesselberg Academy held every three years and devoted to important developments in mathematical ?elds, such as geom- ricanalysis, operatoralgebras, indextheory, andrelatedtopicstogetherwith their applications to mathematical physics. The participants of the conference included mathematicians from fu- tional analysis, di?erential geometry and operator algebras, as well as - perts from mathematical physics interested in A. Connes approach towards the standard model and other physical applications. Thus a large range of topics, from mathematical foundations to recent physical applications, could becoveredinasubstantialway. Theproceedingsofthisconference, organized in a coherent and systematic way, are presented here. Its three chapters c- respond to the main areas discussed during the conference: Chapter1. Foundations of Noncommutative Geometry and Basic Model Building Chapter2. The Lagrangian of the Standard Model Derived from Nonc- mutative Geometry Chapter3. New Directions in Noncommutative Geometry and Mathema- cal Physics During the conference the close interaction between mathematicians and mathematical physicists turned out to be quite fruitful and enlightening for both sides. Similarly, it is hoped that the proceedings presented here will be useful for mathematicians interested in basic physical questions and for physicists aiming at a more conceptual understanding of classical and qu- tum ?eld theory from a novel mathematical point of view."

Spis treści

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.

Blurb

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.