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  - INPR
A1  - Bär, Christian
A1  - Pfäffle, Frank
T1  - Wiener measures on Riemannian manifolds and the Feynman-Kac formula
N2  - This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schrödinger operators with bounded potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)17 
KW  - Wiener measure
KW  - conditional Wiener measure
KW  - Brownian motion
KW  - Brownian bridge
KW  - Riemannian manifold
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59998
ER  -