5797
2012
eng
preprint
1
2012-07-06
--
--
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.
urn:nbn:de:kobv:517-opus-60046
6004
arXiv:1203.5898v1 [math-ph] 27 Mar 2012
RVK-Klassifikation: SI 990
Keine öffentliche Lizenz: Unter Urheberrechtsschutz
Frank Pfäffle
Christoph A. Stephan
Preprints des Instituts für Mathematik der Universität Potsdam
1(2012)20
Mathematik
Spin and Spinc geometry
Spectral theory; eigenvalue problems [See also 47J10, 58E07]
Yang-Mills and other gauge theories
Relativistic gravitational theories other than Einstein`s, including asymmetric field theories
open_access
2012
Institut für Mathematik
Universität Potsdam
https://publishup.uni-potsdam.de/files/5797/premath20_2012.pdf
5793
2012
eng
preprint
1
2012-07-05
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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.
2193-6943
urn:nbn:de:kobv:517-opus-59989
5998
arXiv:1101.1424v3 [math-ph] 3 Jun 2011
RVK-Klassifikation: SI 990
Keine öffentliche Lizenz: Unter Urheberrechtsschutz
Frank Pfäffle
Christoph A. Stephan
Preprints des Instituts für Mathematik der Universität Potsdam
1(2012)16
Mathematik
Spin and Spinc geometry
Spectral theory; eigenvalue problems [See also 47J10, 58E07]
Yang-Mills and other gauge theories
Relativistic gravitational theories other than Einstein`s, including asymmetric field theories
open_access
2012
Institut für Mathematik
Universität Potsdam
https://publishup.uni-potsdam.de/files/5793/premath16_2012.pdf
5796
2012
eng
preprint
1
2012-07-06
--
--
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.
urn:nbn:de:kobv:517-opus-60032
6003
arXiv:1102.0954v4 [math-ph] 27 Mar 2012
RVK-Klassifikation: SI 990
Keine öffentliche Lizenz: Unter Urheberrechtsschutz
Frank Pfäffle
Christoph A. Stephan
Preprints des Instituts für Mathematik der Universität Potsdam
1(2012)19
Mathematik
Spin and Spinc geometry
Spectral theory; eigenvalue problems [See also 47J10, 58E07]
Yang-Mills and other gauge theories
Relativistic gravitational theories other than Einstein`s, including asymmetric field theories
open_access
2012
Institut für Mathematik
Universität Potsdam
https://publishup.uni-potsdam.de/files/5796/premath19_2012.pdf