Dr. Christoph Stephan

ehemaliger Mitarbeiter

Kontakt


Sprechzeiten:
Montags 13-14 Uhr

...

Differentialgeometrie
Lorentzgeometrie
Diracoperatoren und ihre Anwendungen in der Physik
Wärme- und Wellengleichungen
Mathematische Aspekte des Standardmodells
Elastizitätstheorie und Elektro-Elastizitätstheorie

meine Veröffentlichungen auf Google Scholar

 

2008-2011 Postdocstelle finanziert durch die DFG im Rahmen des Programms "Eigene Stelle"
seit 2007 Mitglied im SFB 647 Raum-Zeit-Materie
2005-2007 Fellow der Alexander von Humboldt-Stiftung
2002-2005 Stipendiat der Friedrich Ebert-Stiftung

Vorlesung Lineare Algebra und Analytische Geometrie I

Montag 10:15-11:45, Raum 2.14.0.47
Dienstag 12:15-13:45, Raum 2.14.0.47

Die erste Vorlesung findet Montag den 17. Oktober 2016 statt.

In der Vorlesung werden die Grundkenntnisse der linearen Algebra und analytischen Geometrie vermittelt, die zum Verständnis fast aller Gebiete der Mathematik erforderlich sind. Zum Inhalt der Vorlesung gehören u.a. lineare Gleichungssysteme, Vektorräume, Skalarprodukte, Determinanten und Volumina, Quadriken und Kegelschnitte sowie Eigenwertprobleme.

2016 | Noncommutative Geometry and the Physics of the LHC Era | Christoph Stephan Verlag: Birkhäuser Basel Buchtitel: F. Finster, J. Kleiner, C. Röken, J. Tolksdorf (eds.): Quantum mathematical physics Seiten: 471-495 Link zur Publikation

Noncommutative Geometry and the Physics of the LHC Era

Autoren: Christoph Stephan (2016)

Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and general relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the standard model and reduces the number of degrees of freedom. After an introduction of the basic ideas of Noncommutative geometry, I will present its predictions for the standard model and the few known models beyond the standard model based on a classification scheme for finite spectral triples. Most of these models, including the Standard Model, are now ruled out by LHC data. But interesting extensions of the standard model which agree with the presumed Higgs mass, predict new particles (Fermions, Scalars and Bosons) and await further experimental data.

Verlag:
Birkhäuser Basel
Buchtitel:
F. Finster, J. Kleiner, C. Röken, J. Tolksdorf (eds.): Quantum mathematical physics
Seiten:
471-495

2014 | A Dark Sector Extension of the Almost-Commutative Standard Model | Christoph Stephan Zeitschrift: Int. J. Mod. Phys. A Verlag: World Scientific Seiten: Art. ID 1450005 Band: 29, no. 1 Link zur Publikation, Link zum Preprint

A Dark Sector Extension of the Almost-Commutative Standard Model

Autoren: Christoph Stephan (2014)

We consider an extension of the Standard Model within the frame work of Noncommutative Geometry. The model is based on an older model [St09] 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 ~170 GeV, as predicted by the Spectral Action for the Standard Model, to a value of 120-130 GeV. The short-coming 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.

Zeitschrift:
Int. J. Mod. Phys. A
Verlag:
World Scientific
Seiten:
Art. ID 1450005
Band:
29, no. 1

2013 | Chiral Asymmetry and the Spectral Action | Frank Pfäffle, Christoph Stephan Zeitschrift: Comm. Math. Phys. Verlag: Springer Seiten: 283-310 Band: 321, no. 2 Link zur Publikation, Link zum Preprint

Chiral Asymmetry and the Spectral Action

Autoren: Frank Pfäffle, Christoph Stephan (2013)

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.

Zeitschrift:
Comm. Math. Phys.
Verlag:
Springer
Seiten:
283-310
Band:
321, no. 2

2013 | Noncommutative Geometry in the LHC-Era | Christoph Stephan Buchtitel: Proceedings of the XLVIIIth Rencontres de Moriond EW session Seiten: 451-458 Link zum Preprint

Noncommutative Geometry in the LHC-Era

Autoren: Christoph Stephan (2013)

Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the particle model and reduces the number of degrees of freedom. After briefly introducing the basic ideas of noncommutative geometry, I will present its predictions for the Standard Model and the few known models beyond the Standard Model. Most of these models, including the Standard Model, are now ruled out by LHC data. But interesting extensions of the Standard Model which agree with the presumed Standard Model Scalar mass and predict new particles are still very much alive and await further experimental data.

Buchtitel:
Proceedings of the XLVIIIth Rencontres de Moriond EW session
Seiten:
451-458

2012 | On Gravity, Torsion and the Spectral Action Principle | Frank Pfäffle, Christoph Stephan Zeitschrift: J. Funct. Anal. Verlag: Elsevier Seiten: 1529-1565 Band: 262, no. 4 Link zur Publikation, Link zum Preprint

On Gravity, Torsion and the Spectral Action Principle

Autoren: Frank Pfäffle, Christoph Stephan (2012)

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.

Zeitschrift:
J. Funct. Anal.
Verlag:
Elsevier
Seiten:
1529-1565
Band:
262, no. 4

2011 | The Holst Action by the Spectral Action Principle | Frank Pfäffle, Christoph Stephan Zeitschrift: Comm. Math. Phys. Verlag: Springer Seiten: 261-273 Band: 307, no. 1 Link zur Publikation, Link zum Preprint

The Holst Action by the Spectral Action Principle

Autoren: Frank Pfäffle, Christoph Stephan (2011)

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.

Zeitschrift:
Comm. Math. Phys.
Verlag:
Springer
Seiten:
261-273
Band:
307, no. 1

2010 | The Spectral Action for Dirac Operators with skew-symmetric Torsion | Florian Hanisch, Frank Pfäffle, Christoph Stephan Zeitschrift: Comm. Math. Phys. Verlag: Springer Seiten: 877-888 Band: 300, no. 3 Link zur Publikation, Link zum Preprint

The Spectral Action for Dirac Operators with skew-symmetric Torsion

Autoren: Florian Hanisch, Frank Pfäffle, Christoph Stephan (2010)

We derive a formula for the gravitational part of the spectral action for Dirac operators on 4-dimensional manifolds with totally anti-symmetric torsion. We find that the torsion becomes dynamical and couples to the traceless part of the Riemann curvature tensor. Finally we deduce the Lagrangian for the Standard Model of particle physics in presence of torsion from the Chamseddine-Connes Dirac operator.

Zeitschrift:
Comm. Math. Phys.
Verlag:
Springer
Seiten:
877-888
Band:
300, no. 3

2009 | Das Yang-Mills-Problem. Die mathematische Zähmung des Standardmodells | Christian Bär, Christoph Stephan Zeitschrift: Spektrum der Wissenschaft Verlag: Spektrum der Wissenschaft Verlag Seiten: 66-73 Band: 5 Link zur Publikation

Das Yang-Mills-Problem. Die mathematische Zähmung des Standardmodells

Autoren: Christian Bär, Christoph Stephan (2009)

Die moderne Theorie der Elementarteilchen, die Quanten-Yang-Mills-Theorie, vermag die experimentellen Befunde mit unerhörter Genauigkeit wiederzugegen, es fehlt ihr jedoch bisher ein solides mathematisches Fundament. Über dessen Gestalt gibt es nur sehr nebelhafte Vorstellungen.

Zeitschrift:
Spektrum der Wissenschaft
Verlag:
Spektrum der Wissenschaft Verlag
Seiten:
66-73
Band:
5

2009 | On a classification of irreducible almost-commutative geometries V | Jan-Hendrik Jureit, Christoph Stephan Zeitschrift: J. Math. Phys. Verlag: American Institute of Physics Seiten: 72301 Band: 50, no. 7 Link zur Publikation, Link zum Preprint

On a classification of irreducible almost-commutative geometries V

Autoren: Jan-Hendrik Jureit, Christoph Stephan (2009)

We extend a classification of irreducible, almost-commutative geometries whose spectral action is dynamically non-degenerate, 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 electro-strong model and a variety of the electro-strong model with Higgs mechanism.

Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
Seiten:
72301
Band:
50, no. 7

2009 | New Scalar Fields in Noncommutative Geometry | Christoph Stephan Zeitschrift: Phys. Rev. D Verlag: American Physical Society Seiten: 65013 Band: 79, no. 6 Link zur Publikation, Link zum Preprint

New Scalar Fields in Noncommutative Geometry

Autoren: Christoph Stephan (2009)

In this publication we present an extension of the Standard Model within the framework of Connes' noncommutative geometry [1]. The model presented here is based on a minimal spectral triple [7] 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 [1] which also determines relations among the gauge couplings, the quartic scalar couplings and the Yukawa couplings at a cut-off energy of ca. 10^(17) GeV. We investigate the renormalisation group flow of these relations. The low energy behaviour allows to constrain the Higgs mass, the mass of the new scalar and the mixing between these two scalar fields.

Zeitschrift:
Phys. Rev. D
Verlag:
American Physical Society
Seiten:
65013
Band:
79, no. 6

2009 | Krajewski diagrams and the Standard Model | Christoph Stephan Zeitschrift: J. Math. Phys Verlag: American Institute of Physics Seiten: 43515 Band: 50, no. 4 Link zur Publikation, Link zum Preprint

Krajewski diagrams and the Standard Model

Autoren: Christoph Stephan (2009)

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.

Zeitschrift:
J. Math. Phys
Verlag:
American Institute of Physics
Seiten:
43515
Band:
50, no. 4

2009 | Beyond the Standard Model: A Noncommutative Approach | Christoph Stephan Buchtitel: Proceedings of the XLIVth Rencontres de Moriond: Electroweak Interactions and Unified Theories Link zum Preprint

Beyond the Standard Model: A Noncommutative Approach

Autoren: Christoph Stephan (2009)

During the last two decades Alain Connes developed Noncommutative Geometry (NCG), which allows to unify two of the basic theories of modern physics: General Relativity (GR) and the Standard Model (SM) of Particle Physics as classical field theories. In the noncommutative framework the Higgs boson, which had previously to be put in by hand, and many of the ad hoc features of the standard model appear in a natural way.
The aim of this presentation is to motivate this unification from basic physical principles and to give a flavour of its derivation. One basic prediction of the noncommutative approach to the SM is that the mass of the Higgs Boson should be of the order of 170 GeV if one assumes the Big Desert. This mass range is with reasonable probability excluded by the Tevatron and therefore it is interesting to investigate models beyond the SM that are compatible with NCG. Going beyond the SM is highly non-trivial within the NCG approach but possible extensions have been found and provide for phenomenologically interesting models. We will present in this article a short introduction into the NCG framework and describe one of these extensions of the SM. This model contains new scalar bosons (and fermions) which constitute a second Higgs-like sector mixing with theordinary Higgs sector and thus considerably modifying the mass eigenvalues.

Buchtitel:
Proceedings of the XLIVth Rencontres de Moriond: Electroweak Interactions and Unified Theories

2009 | The Inverse Seesaw Mechanism in Noncommutative Geometry | Christoph Stephan Zeitschrift: Phys. Rev. D Verlag: American Physical Society Seiten: 65007 Band: 80, no. 6 Link zur Publikation, Link zum Preprint

The Inverse Seesaw Mechanism in Noncommutative Geometry

Autoren: Christoph Stephan (2009)

In this publication 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 to the classical AC model is the chiral nature of the AC fermions with respect to a U(1) 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 (ca. 1 GeV to 10^6 GeV). From this configuration a working inverse Seesaw mechanism for the neutrinos is obtained.

Zeitschrift:
Phys. Rev. D
Verlag:
American Physical Society
Seiten:
65007
Band:
80, no. 6

2008 | Finding the standard model of particle physics: A combinatorial problem | Jan-Hendrik Jureit, Christoph Stephan Zeitschrift: Comput. Phys. Commun. Verlag: Elsevier Seiten: 230-247 Band: 178, no. 3 Link zur Publikation, Link zum Preprint

Finding the standard model of particle physics: A combinatorial problem

Autoren: Jan-Hendrik Jureit, Christoph Stephan (2008)

We present a combinatorial problem which consists in finding irreducible Krajewski diagrams from finite geometries. This problem boils down to placing arrows into a quadratic array with some additional constrains. The Krajewski diagrams play a central role in the description of finite noncommutative geometries. They allow to localise the standard model of particle physics within the set of all Yang-Mills-Higgs models.

Zeitschrift:
Comput. Phys. Commun.
Verlag:
Elsevier
Seiten:
230-247
Band:
178, no. 3

2008 | On a classification of irreducible almost-commutative geometries. IV | Jan-Hendrik Jureit, Christoph Stephan Zeitschrift: J. Math. Phys. Verlag: American Institute of Physics Seiten: 33502 Band: 49, no. 3 Link zur Publikation, Link zum Preprint

On a classification of irreducible almost-commutative geometries. IV

Autoren: Jan-Hendrik Jureit, Christoph Stephan (2008)

In this paper we will classify the finite spectral triples with KO-dimension six, following the classification found in [1,2,3,4], with up to four summands in the matrix algebra. Again, heavy use is made of Krajewski diagrams [5]. Furthermore we will show that any real finite spectral triple in KO-dimension 6 is automatically S 0 -real. This work has been inspired by the recent paper by Alain Connes [6] and John Barrett [7].
In the classification we find that the standard model of particle physics in its minimal version fits the axioms of noncommutative geometry in the case of KO-dimension six. By minimal version it is meant that at least one neutrino has to be massless and mass-terms mixing particles and antiparticles are prohibited

Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
Seiten:
33502
Band:
49, no. 3

2008 | Gauge unification in noncommutative geometry | Christoph Stephan Zeitschrift: Europhys. Lett. Verlag: IOP Publishing Seiten: 51003 Band: 84 Link zur Publikation, Link zum Preprint

Gauge unification in noncommutative geometry

Autoren: Christoph Stephan (2008)

Gauge unification is widely considered to be a desirable feature for extensions of the standard model. Unfortunately the standard model itself does not exhibit a unification of its running gauge couplings but it is required by grand unified theories as well as the noncommutative version of the standard model [2].
We will consider here the extension of the noncommutative standard model by vector doublets as proposed in [6]. Two consequences of this modification are: 1. the relations of the coupling constants at unification energy are altered with respect to the well known relation from grand unified theories. 2. The extended model allows for unification of the gauge couplings at ~10^(13) GeV.

Zeitschrift:
Europhys. Lett.
Verlag:
IOP Publishing
Seiten:
51003
Band:
84

2007 | Seesaw and noncommutative geometry | Jan-Hendrik Jureit, Thomas Krajewski, Thomas Schucker, Christoph Stephan Zeitschrift: Phys. Lett. B Verlag: Elsevier Seiten: 127-132 Band: 654, no. 3 Link zur Publikation, Link zum Preprint

Seesaw and noncommutative geometry

Autoren: Jan-Hendrik Jureit, Thomas Krajewski, Thomas Schucker, Christoph Stephan (2007)

The 1-loop corrections to the seesaw mechanism in the noncommutative standard model are computed. Other consequences of the Lorentzian signature in the inner space are summarised.

Zeitschrift:
Phys. Lett. B
Verlag:
Elsevier
Seiten:
127-132
Band:
654, no. 3

2007 | On the noncommutative standard model | Jan-Hendrik Jureit, Thomas Krajewski, Thomas Schucker, Christoph Stephan Zeitschrift: Acta Phys. Polon. B Verlag: Jagiellonian University, Poland Seiten: 3181-3202 Band: 38, no. 10 Link zur Publikation, Link zum Preprint

On the noncommutative standard model

Autoren: Jan-Hendrik Jureit, Thomas Krajewski, Thomas Schucker, Christoph Stephan (2007)

We propose a pedestrian review of the noncommutative standard model in its present state.

Zeitschrift:
Acta Phys. Polon. B
Verlag:
Jagiellonian University, Poland
Seiten:
3181-3202
Band:
38, no. 10

2007 | Almost-commutative geometries beyond the Standard Model III: Vector Doublets | Romain Squellari, Christoph Stephan Zeitschrift: J. Phys. A Verlag: IOP Publishing Seiten: 10685-10698 Band: 40, no. 34 Link zur Publikation, Link zum Preprint

Almost-commutative geometries beyond the Standard Model III: Vector Doublets

Autoren: Romain Squellari, Christoph Stephan (2007)

We will present a new extension of the standard model of particle physics in its almostcommutative formulation. This extension has as its basis the algebra of the standard model with four summands [11], and enlarges only the particle content by an arbitrary number of generations of left-right symmetric doublets which couple vectorially to the U(1)YxSU(2)w subgroup of the standard model. As in the model presented in [8], which introduced particles with a new colour, grand unification is no longer required by the spectral action. The new model may also possess a candidate for dark matter in the hundred TeV mass range with neutrino-like cross section.

Zeitschrift:
J. Phys. A
Verlag:
IOP Publishing
Seiten:
10685-10698
Band:
40, no. 34

2007 | Massive neutrinos in almost commutative geometry | Christoph Stephan Zeitschrift: J. Math. Phys. Verlag: American Institute of Physics Seiten: 23513 Band: 48 Link zur Publikation, Link zum Preprint

Massive neutrinos in almost commutative geometry

Autoren: Christoph Stephan (2007)

In the noncommutative formulation of the standard model of particle physics by A. Connes and A. Chamseddine [1] one of the three generations of fermions has to possess a massless neutrino. This formulation is consistent with neutrino oscillation experiments and the known bounds of the Pontecorvo-Maki-Nakagawa-Sakata matrix (PMNS matrix). But future experiments which may be able to detect neutrino masses directly and high-precission measurements of the PMNS matrix might need massive neutrinos in all three generations.
In this publication we present an almost-commutative geometry which allows for a standard model with massive neutrinos in all three generations. This model does not follow in a straight forward way from Connes' and Chamseddine's version since it requires an internal algebra with four summands of matrix algebras, instead of three summands for the model with one massless neutrino.

Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
Seiten:
23513
Band:
48

2007 | Almost-commutative geometries beyond the Standard Model II: New Colours | Christoph Stephan Zeitschrift: J. Phys. A Verlag: IOP Publishing Seiten: 9941-9956 Band: 40, no. 32 Link zur Publikation, Link zum Preprint

Almost-commutative geometries beyond the Standard Model II: New Colours

Autoren: Christoph Stephan (2007)

We will present an extension of the standard model of particle physics in its almost-commutative formulation. This extension is guided by the minimal approach to almost-commutative geometries employed in [13], although the model presented here is not minimal itself.
The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model and two new fermions of opposite electro-magnetic charge which may possess a new colour like gauge group. As a new phenomenon, grand unification is no longer required by the spectral action.

Zeitschrift:
J. Phys. A
Verlag:
IOP Publishing
Seiten:
9941-9956
Band:
40, no. 32

2006 | Cold dark matter by heavy double charged leptons? | Daniele Fargion, Maxim Khlopov, Christoph Stephan Zeitschrift: Class. Quantum Grav. Verlag: IOP Publishing Seiten: 7305-7354 Band: 23, no. 24 Link zur Publikation, Link zum Preprint

Cold dark matter by heavy double charged leptons?

Autoren: Daniele Fargion, Maxim Khlopov, Christoph Stephan (2006)

A new candidate of cold dark matter arises by a novel elementary particle model: the almostcommutative AC-geometrical framework. Two heavy leptons are added to the Standard Model, each one sharing a double opposite electric charge and an own lepton flavor number The novel mathematical theory of almost-commutative geometry [1] wishes to unify gauge models with gravity. In this scenario two new heavy (m_L>100GeV), oppositely double charged leptons (A,C),(A with charge -2 and C with charge +2), are born with no twin quark companions. The model naturally involves a new U(1) gauge interaction, possessed only by the AC-leptons and providing a Coulomblike attraction between them. AC-leptons posses electro-magnetic as well as Z-boson interaction and, according to the charge chosen for the new U(1) gauge interaction, a new "invisible light" interaction. Their final cosmic relics are bounded into "neutral" stable atoms (AC) forming the mysterious cold dark matter, in the spirit of the Glashow's Sinister model. An (AC) state is reached in the early Universe along a tail of a few secondary frozen exotic components. They should be now here somehow hidden in the surrounding matter. The two main secondary manifest relics are C (mostly hidden in a neutral (Cee) "anomalous helium" atom, at a 10-8 ratio) and a corresponding "ion" A bounded with an ordinary helium ion (4He); indeed the positive helium ions are able to attract and capture the free A fixing them into a neutral relic cage that has nuclear interaction (4HeA).

Zeitschrift:
Class. Quantum Grav.
Verlag:
IOP Publishing
Seiten:
7305-7354
Band:
23, no. 24

2006 | Composite dark matter with invisible light from almost-commutative geometry | Maxim Khlopov, Christoph Stephan Link zum Preprint

Composite dark matter with invisible light from almost-commutative geometry

Autoren: Maxim Khlopov, Christoph Stephan (2006)

Almost commutative geometry offers a specific way to unify general relativity, quantum mechanics and gauge symmetries. The AC-model of elementary particles, arising on this way, naturally embeds the Standard model and predicts doubly charged AC-leptons, anion-like A^{--} and cathion-like C^{++}, which can bind in WIMP-like (AC)-atoms, being a nontrivial candidate for cosmological dark matter. This state is reached in the early Universe along a tail of more manifest secondary frozen blocks. They should be now here polluting the surrounding matter. The main secondary relics are C^{++} "anomalous helium" and a bound system of A^{--} with an ordinary helium ion (^4He)^{++}, which is able to attract and capture (in thefirst three minutes) all the free A^{--} fixing them into a neutral OLe-helium (OHe) nuclear interacting "atom" (^4He^{++}A^{--}). The model naturally involves a new U(1) gauge interaction, possessed only by the AC-leptons and providing a Coulomb-like attraction between them. This attraction stimulates the effective A-C recombination into AC-atoms inside dense matter bodies (stars and planets), resulting in a decrease of anomalous isotopes below the experimental upper limits. OLe-helium pollution of terrestrial matter and (OHe) catalysis of nuclear reactions in it is one of the exciting problems (or advantages?) of the present model.

2006 | Almost-commutative geometries beyond the Standard Model | Christoph Stephan Zeitschrift: J. Phys. A Verlag: IOP Publishing Seiten: 9657-9670 Band: 39, no. 30 Link zur Publikation, Link zum Preprint

Almost-commutative geometries beyond the Standard Model

Autoren: Christoph Stephan (2006)

In [7-9] and [10] the conjecture is presented that almost-commutative geometries, with respect to sensible physical constraints, allow only the standard model of particle physics and electro-strong models as Yang-Mills-Higgs theories. In this publication a counter example will be given.
The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model of particle physics and two new fermions of opposite electro-magnetic charge. This is the second Yang-Mills-Higgs model within noncommutative geometry, after the standard model, which could be compatible with experiments. Combined to a hydrogen-like composite particle these new particles provide a novel dark matter candidate.

Zeitschrift:
J. Phys. A
Verlag:
IOP Publishing
Seiten:
9657-9670
Band:
39, no. 30

2006 | Almost-commutative geometry, massive neutrinos and the orientability axiom in KO-dimension 6 | Christoph Stephan Link zum Preprint

Almost-commutative geometry, massive neutrinos and the orientability axiom in KO-dimension 6

Autoren: Christoph Stephan (2006)

In recent publications Alain Connes [1] and John Barrett [2] proposed to change the KO-dimension of the internal space of the standard model in its noncommutative representation [3] from zero to six. This apparently minor modification allowed to resolve the fermion doubling problem [4], and the introduction of Majorana mass terms for the right-handed neutrino. The price which had to be paid was that at least the orientability axiom of noncommutative geometry [5,6] may not be obeyed by the underlying geometry. In this publication we review three internal geometries, all three failing to meet the orientability axiom of noncommutative geometry. They will serve as examples to illustrate the nature of this lack of orientability. We will present an extension of the minimal standard model found in [7] by a right-handed neutrino, where only the sub-representation associated to this neutrino is not orientable.

2005 | On a classification of irreducible almost commutative geometries. III | Jan-Hendrik Jureit, Thomas Schucker, Christoph Stephan Zeitschrift: J. Math. Phys. Verlag: American Institute of Physics Seiten: 72303 Band: 46, no. 7 Link zur Publikation, Link zum Preprint

On a classification of irreducible almost commutative geometries. III

Autoren: Jan-Hendrik Jureit, Thomas Schucker, Christoph Stephan (2005)

We extend a classification of irreducible, almost commutative geometries whose spectral action is dynamically non-degenerate to internal algebras that have four simple summands.

Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
Seiten:
72303
Band:
46, no. 7

2005 | On a classification of irreducible almost commutative geometries, a second helping | Jan-Hendrik Jureit, Christoph Stephan Zeitschrift: J. Math. Phys. Verlag: American Institute of Physics Seiten: 43512 Band: 46, no. 4 Link zur Publikation, Link zum Preprint

On a classification of irreducible almost commutative geometries, a second helping

Autoren: Jan-Hendrik Jureit, Christoph Stephan (2005)

We complete the classification of almost commutative geometries from a particle physics point of view given in hep-th/0312276. Four missing Krajewski diagrams will be presented after a short introduction into irreducible, non-degenerate spectral triples.

Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
Seiten:
43512
Band:
46, no. 4

2004 | On a classification of irreducible almost commutative geometries | Bruno Iochum, Thomas Schucker, Christoph Stephan Zeitschrift: J. Math. Phys. Verlag: American Institute of Physics Seiten: 5003-5041 Band: 45, no. 12 Link zur Publikation, Link zum Preprint

On a classification of irreducible almost commutative geometries

Autoren: Bruno Iochum, Thomas Schucker, Christoph Stephan (2004)

We classify all irreducible, almost commutative geometries whose spectral action is dynamically non-degenerate. Heavy use is made of Krajewski's diagrammatic language. The motivation for our definition of dynamical non-degeneracy stems from particle physics where the fermion masses are non-degenerate.

Zeitschrift:
J. Math. Phys.
Verlag:
American Institute of Physics
Seiten:
5003-5041
Band:
45, no. 12