@unpublished{PfaeffleStephan2012,
  author    = {Pf{\"a}ffle, Frank and Stephan, Christoph A.},
  title     = {On gravity, torsion and the spectral action principle},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59989},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}
@unpublished{PfaeffleStephan2012,
  author    = {Pf{\"a}ffle, Frank and Stephan, Christoph A.},
  title     = {The Holst action by the spectral action principle},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60032},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}
@unpublished{PfaeffleStephan2012,
  author    = {Pf{\"a}ffle, Frank and Stephan, Christoph A.},
  title     = {Chiral asymmetry and the spectral action},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60046},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}