Noncommutative Geometry and the Standard Model of Elementary Particle PhysicsFlorian Scheck, Wend Werner, Harald Upmeier Springer, 11 jan 2008 - 350 pagina's 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. |
Inhoudsopgave
| 4 | |
| 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 |
Overige edities - Alles bekijken
Noncommutative Geometry and the Standard Model of Elementary Particle Physics Florian Scheck,Wend Werner,Harald Upmeier Gedeeltelijke weergave - 2002 |
Noncommutative Geometry and the Standard Model of Elementary Particle Physics Florian Scheck,Wend Werner,Harald Upmeier Geen voorbeeld beschikbaar - 2010 |
Noncommutative Geometry and the Standard Model of Elementary Particle Physics Florian Scheck,Wend Werner,Harald Upmeier Geen voorbeeld beschikbaar - 2002 |
Veelvoorkomende woorden en zinsdelen
1-forms assertion follows asymptotic bosonic C*-algebra CB(H Cl(M classical Clifford algebra commutative compact operators connection Connes consider constructed Corollary corresponding covariant curvature defined definition denote diffeomorphisms dimension Dirac operator Dixmier trace eigenvalues elements endomorphisms equations Euclidean fermion finite rank formula function gauge fields gauge transformations given graded heat kernel Hence Higgs Hilbert space Hopf algebra ideal implies inner product integral interaction invariant isometry isomorphism Lagrangian Lemma leptons Lie algebra mass matrix multiplication NC gauge non-trivial noncommutative geometry notation obtain orthonormal orthoprojection particles physical positive Proof Proposition quarks Rabcd real spectral triple real structure renormalization representation Riemannian manifold scalar product Scheck Section smooth spacetime spectral action spin spinor bundle Standard Model string summand symmetry tensor product Theorem trace class trivial Upmeier vector bundle vector fields Yang-Mills