@article{PfaeffleStephan2013,
  author    = {Pf{\"a}ffle, Frank and Stephan, Christoph A.},
  title     = {Chiral asymmetry and the spectral action},
  series = {Communications in mathematical physics},
  volume    = {321},
  journal   = {Communications in mathematical physics},
  number    = {2},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-012-1641-6},
  pages     = {283 -- 310},
  year      = {2013},
  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}
}
@article{PfaeffleStephan2012,
  author    = {Pf{\"a}ffle, Frank and Stephan, Christoph A.},
  title     = {On gravity, torsion and the spectral action principle},
  series = {Journal of functional analysis},
  volume    = {262},
  journal   = {Journal of functional analysis},
  number    = {4},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-1236},
  doi       = {10.1016/j.jfa.2011.11.013},
  pages     = {1529 -- 1565},
  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}
}
@article{PfaeffleStephan2011,
  author    = {Pf{\"a}ffle, Frank and Stephan, Christoph A.},
  title     = {The holst action by the spectral action principle},
  series = {Communications in mathematical physics},
  volume    = {307},
  journal   = {Communications in mathematical physics},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-011-1303-0},
  pages     = {261 -- 273},
  year      = {2011},
  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}
}
@misc{PfaeffleStephan2012,
  author    = {Pf{\"a}ffle, Frank and Stephan, Christoph A.},
  title     = {The holst action by the spectral action principle (vol 307, pg 261, 2011)},
  series = {Communications in mathematical physics},
  volume    = {313},
  journal   = {Communications in mathematical physics},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-012-1507-y},
  pages     = {291 -- 292},
  year      = {2012},
  language  = {en}
}
@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}
}
@article{Pfaeffle2005,
  author    = {Pf{\"a}ffle, Frank},
  title     = {Eigenvalues of Dirac Operators for Hyperbolic Degenerations},
  year      = {2005},
  abstract  = {We study the behaviour of the spectrum of the Dirac operator for sequences of compact hyperbolic manifolds whose limit is non-compact. If the spectrum of the limit manifold is descrete we show that the spectrum is approximated by the spectra of compact manifolds.},
  language  = {en}
}
@article{PfaffleWeiss2009,
  author    = {Pfaffle, Frank and Weiss, Hartmut},
  title     = {The Laplacian on hyperbolic 3-manifolds with Dehn surgery type singularities},
  issn      = {1019-8385},
  year      = {2009},
  abstract  = {We study the spectrum of the Laplacian on hyperbolic 3-manifolds with Dehn surgery type singularities and its dependence on the generalized Dehn surgery coefficients.},
  language  = {en}
}
@unpublished{BaerPfaeffle2012,
  author    = {B{\"a}r, Christian and Pf{\"a}ffle, Frank},
  title     = {Wiener measures on Riemannian manifolds and the Feynman-Kac formula},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59998},
  year      = {2012},
  abstract  = {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 Schr{\"o}dinger 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.},
  language  = {en}
}