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Chiral asymmetry and the spectral action

  • We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter.

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Author:Frank Pfäffle, Christoph A. Stephan
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (1(2012)20)
Document Type:Preprint
Year of Completion:2012
Publishing Institution:Universität Potsdam
Release Date:2012/07/06
Source:arXiv:1203.5898v1 [math-ph] 27 Mar 2012
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53Cxx Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx] / 53C27 Spin and Spinc geometry
58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Cxx Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx] / 58C40 Spectral theory; eigenvalue problems [See also 47J10, 58E07]
70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX) / 70Sxx Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83- XX] / 70S15 Yang-Mills and other gauge theories
83-XX RELATIVITY AND GRAVITATIONAL THEORY / 83Dxx Relativistic gravitational theories other than Einstein`s, including asymmetric field theories / 83D05 Relativistic gravitational theories other than Einstein`s, including asymmetric field theories
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:RVK-Klassifikation: SI 990