TY - GEN
A1 - Pfäffle, Frank
A1 - Stephan, Christoph A.
T1 - The holst action by the spectral action principle (vol 307, pg 261, 2011)
T2 - Communications in mathematical physics
Y1 - 2012
U6 - http://dx.doi.org/10.1007/s00220-012-1507-y
SN - 0010-3616 (print)
VL - 313
IS - 1
SP - 291
EP - 292
PB - Springer
CY - New York
ER -
TY - JOUR
A1 - Pfäffle, Frank
A1 - Stephan, Christoph A.
T1 - Chiral asymmetry and the spectral action
JF - Communications in mathematical physics
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.
Y1 - 2013
U6 - http://dx.doi.org/10.1007/s00220-012-1641-6
SN - 0010-3616 (print)
SN - 1432-0916 (online)
VL - 321
IS - 2
SP - 283
EP - 310
PB - Springer
CY - New York
ER -
TY - JOUR
A1 - Pfäffle, Frank
A1 - Stephan, Christoph A.
T1 - On gravity, torsion and the spectral action principle
JF - Journal of functional analysis
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.
KW - Orthogonal connections with torsion
KW - Spectral triples
KW - Commutative geometries
KW - Chamseddine-Connes spectral action
Y1 - 2012
U6 - http://dx.doi.org/10.1016/j.jfa.2011.11.013
SN - 0022-1236 (print)
VL - 262
IS - 4
SP - 1529
EP - 1565
PB - Elsevier
CY - San Diego
ER -
TY - JOUR
A1 - Pfäffle, Frank
A1 - Stephan, Christoph A.
T1 - The holst action by the spectral action principle
JF - Communications in mathematical physics
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.
Y1 - 2011
U6 - http://dx.doi.org/10.1007/s00220-011-1303-0
SN - 0010-3616 (print)
VL - 307
IS - 1
SP - 261
EP - 273
PB - Springer
CY - New York
ER -
TY - JOUR
A1 - Jureit, Jan-Hendrik
A1 - Stephan, Christoph A.
T1 - On a classification of irreducible almost-commutative geometries V
N2 - 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.
Y1 - 2009
UR - http://jmp.aip.org/
U6 - http://dx.doi.org/10.1063/1.3167287
SN - 0022-2488
ER -
TY - JOUR
A1 - Stephan, Christoph A.
T1 - Inverse seesaw mechanism in noncommutative geometry
N2 - 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.
Y1 - 2009
UR - http://prd.aps.org/
U6 - http://dx.doi.org/10.1103/Physrevd.80.065007
SN - 1550-7998
ER -
TY - JOUR
A1 - Stephan, Christoph A.
T1 - Krajewski diagrams and the standard model
N2 - This paper provides a complete list of Krajewski diagrams representing the standard model of particle physics. We will give the possible representations of the algebra and the anomaly free lifts which provide the representation of the standard model gauge group on the fermionic Hilbert space. The algebra representations following from the Krajewski diagrams are not complete in the sense that the corresponding spectral triples do not necessarily obey to the axiom of Poincare duality. This defect may be repaired by adding new particles to the model, i.e., by building models beyond the standard model. The aim of this list of finite spectral triples (up to Poincare duality) is therefore to provide a basis for model building beyond the standard model.
Y1 - 2009
UR - http://jmp.aip.org/
U6 - http://dx.doi.org/10.1063/1.3112622
SN - 0022-2488
ER -
TY - JOUR
A1 - Stephan, Christoph A.
T1 - New scalar fields in noncommutative geometry
N2 - In this publication we present an extension of the standard model within the framework of Connes' noncommutative geometry. The model presented here is based on a minimal spectral triple which contains the standard model particles, new vectorlike fermions, and a new U(1) gauge subgroup. Additionally a new complex scalar field appears that couples to the right-handed neutrino, the new fermions, and the standard Higgs particle. The bosonic part of the action is given by the spectral action which also determines relations among the gauge couplings, the quartic scalar couplings, and the Yukawa couplings at a cutoff energy of similar to 10(17) GeV. We investigate the renormalization group flow of these relations. The low energy behavior allows to constrain the Higgs mass, the mass of the new scalar, and the mixing between these two scalar fields.
Y1 - 2009
UR - http://prd.aps.org/
U6 - http://dx.doi.org/10.1103/Physrevd.79.065013
SN - 1550-7998
ER -
TY - JOUR
A1 - Stephan, Christoph A.
T1 - A dark sector extension of the almost-commutative standard model
JF - International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics
N2 - 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.
KW - Noncommutative geometry
KW - spectral triple
KW - beyond Standard Model
KW - Higgs boson
KW - scalar fields
Y1 - 2014
U6 - http://dx.doi.org/10.1142/S0217751X14500055
SN - 0217-751X (print)
SN - 1793-656X (online)
VL - 29
IS - 1
PB - World Scientific
CY - Singapore
ER -