Noncommutative Geometry and the Standard Model of Elementary Particle Physics

Voorkant
Florian Scheck, Wend Werner, Harald Upmeier
Springer Science & Business Media, 26 nov. 2002 - 350 pagina's
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.
 

Wat mensen zeggen - Een review schrijven

We hebben geen reviews gevonden op de gebruikelijke plaatsen.

Inhoudsopgave

1 Spectral Triples and Abstract YangMills Functional
4
2 Real Spectral Triples and Charge Conjugation
11
Spinors Dirac Operator and de Rham Algebra
21
4 Connes Trace Formula and Dirac Realization of Maxwell and YangMills Action
40
5 The EinsteinHilbert Action as a Spectral Action
75
6 Spectral Action and the ConnesChamsedinne Model
109
7 Dirac Operator and Real Structure on Euclidean and Minkowski Spacetime
134
8 The Electroweak Model
152
11 The Higgs Mechanism and Spontaneous Symmetry Breaking
230
12 The Impact of NC Geometry in Particle Physics
242
13 The su21 Model of Electroweak Interactions and Its Connection to NC Geometry
260
14 Quantum Fields and Noncommutative Spacetime
271
Simple Examples
278
16 Dirac Eigenvalues as Dynamical Variables
299
17 Hopf Algebras in Renormalization and NC Geometry
313
18 NC Geometry of Strings and Duality Symmetry
325

9 The Full Standard Model
172
10 Standard Model Coupled with Gravity
216

Overige edities - Alles weergeven

Veelvoorkomende woorden en zinsdelen

Bibliografische gegevens