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On gravity, torsion and the spectral action principle

  • We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally anti-symmetric torsion we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points.

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Author:Frank Pfäffle, Christoph A. Stephan
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (1(2012)16)
Document Type:Preprint
Year of Completion:2012
Publishing Institution:Universität Potsdam
Release Date:2012/07/05
Source:arXiv:1101.1424v3 [math-ph] 3 Jun 2011
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