TY - JOUR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - The holst action by the spectral action principle JF - Communications in mathematical physics N2 - 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. Y1 - 2011 U6 - https://doi.org/10.1007/s00220-011-1303-0 SN - 0010-3616 VL - 307 IS - 1 SP - 261 EP - 273 PB - Springer CY - New York ER - TY - JOUR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - On gravity, torsion and the spectral action principle JF - Journal of functional analysis N2 - 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. KW - Orthogonal connections with torsion KW - Spectral triples KW - Commutative geometries KW - Chamseddine-Connes spectral action Y1 - 2012 U6 - https://doi.org/10.1016/j.jfa.2011.11.013 SN - 0022-1236 VL - 262 IS - 4 SP - 1529 EP - 1565 PB - Elsevier CY - San Diego ER - TY - GEN A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - The holst action by the spectral action principle (vol 307, pg 261, 2011) T2 - Communications in mathematical physics Y1 - 2012 U6 - https://doi.org/10.1007/s00220-012-1507-y SN - 0010-3616 VL - 313 IS - 1 SP - 291 EP - 292 PB - Springer CY - New York ER - TY - INPR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - On gravity, torsion and the spectral action principle N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)16 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59989 SN - 2193-6943 ER - TY - INPR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - The Holst action by the spectral action principle N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)19 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60032 ER - TY - INPR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - Chiral asymmetry and the spectral action N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)20 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60046 ER - TY - JOUR A1 - Pfäffle, Frank A1 - Stephan, Christoph A. T1 - Chiral asymmetry and the spectral action JF - Communications in mathematical physics N2 - 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. Y1 - 2013 U6 - https://doi.org/10.1007/s00220-012-1641-6 SN - 0010-3616 SN - 1432-0916 VL - 321 IS - 2 SP - 283 EP - 310 PB - Springer CY - New York ER -