@article{Stephan2014,
author = {Stephan, Christoph A.},
title = {A dark sector extension of the almost-commutative standard model},
series = {International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics},
volume = {29},
journal = {International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics},
number = {1},
publisher = {World Scientific},
address = {Singapore},
issn = {0217-751X (print)},
doi = {10.1142/S0217751X14500055},
pages = {30},
year = {2014},
abstract = {We consider an extension of the Standard Model within the framework of Noncommutative Geometry. The model is based on an older model [C. A. Stephan, Phys. Rev. D 79, 065013 (2009)] which extends the Standard Model by new fermions, a new U(1)-gauge group and, crucially, a new scalar field which couples to the Higgs field. This new scalar field allows to lower the mass of the Higgs mass from similar to 170 GeV, as predicted by the Spectral Action for the Standard Model, to a value of 120-130 GeV. The shortcoming of the previous model lay in its inability to meet all the constraints on the gauge couplings implied by the Spectral Action. These shortcomings are cured in the present model which also features a "dark sector" containing fermions and scalar particles.},
language = {en}
}
@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 (print)},
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}
}
@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 (print)},
doi = {10.1007/s00220-012-1507-y},
pages = {291 -- 292},
year = {2012},
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 (print)},
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}
}
@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{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 (print)},
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}
}
@article{JureitStephan2009,
author = {Jureit, Jan-Hendrik and Stephan, Christoph A.},
title = {On a classification of irreducible almost-commutative geometries V},
issn = {0022-2488},
doi = {10.1063/1.3167287},
year = {2009},
abstract = {We extend a classification of irreducible almost-commutative geometries, whose spectral action is dynamically nondegenerate, to internal algebras that have six simple summands. We find essentially four particle models: an extension of the standard model by a new species of fermions with vectorlike coupling to the gauge group and gauge invariant masses, two versions of the electrostrong model, and a variety of the electrostrong model with Higgs mechanism.},
language = {en}
}
@article{Stephan2009,
author = {Stephan, Christoph A.},
title = {Inverse seesaw mechanism in noncommutative geometry},
issn = {1550-7998},
doi = {10.1103/Physrevd.80.065007},
year = {2009},
abstract = {In this paper we will implement the inverse seesaw mechanism into the noncommutative framework on the basis of the AC extension of the standard model. The main difference from the classical AC model is the chiral nature of the AC fermions with respect to a U(1)(X) extension of the standard model gauge group. It is this extension which allows us to couple the right-handed neutrinos via a gauge invariant mass term to left-handed A particles. The natural scale of these gauge invariant masses is of the order of 10(17) GeV while the Dirac masses of the neutrino and the AC particles are generated dynamically and are therefore much smaller (similar to 1 to similar to 10(6) GeV). From this configuration, a working inverse seesaw mechanism for the neutrinos is obtained.},
language = {en}
}