The Holst action by the spectral action principle

  • We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.

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Metadaten
Author details:Frank Pfäffle, Christoph A. Stephan
URN:urn:nbn:de:kobv:517-opus-60032
Publication series (Volume number):Preprints des Instituts für Mathematik der Universität Potsdam (1(2012)19)
Publication type:Preprint
Language:English
Publication year:2012
Publishing institution:Universität Potsdam
Release date:2012/07/06
Source:arXiv:1102.0954v4 [math-ph] 27 Mar 2012
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC 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
Collection(s):Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
License (German):License LogoKeine öffentliche Lizenz: Unter Urheberrechtsschutz
External remark:RVK-Klassifikation: SI 990
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