43 research outputs found
Quantum field theory on projective modules
We propose a general formulation of perturbative quantum field theory on
(finitely generated) projective modules over noncommutative algebras. This is
the analogue of scalar field theories with non-trivial topology in the
noncommutative realm. We treat in detail the case of Heisenberg modules over
noncommutative tori and show how these models can be understood as large
rectangular pxq matrix models, in the limit p/q->theta, where theta is a
possibly irrational number. We find out that the modele is highly sensitive to
the number-theoretical aspect of theta and suffers from an UV/IR-mixing. We
give a way to cure the entanglement and prove one-loop renormalizability.Comment: 52 pages, uses feynm
Quasi-quantum groups from Kalb-Ramond fields and magnetic amplitudes for strings on orbifolds
We present the general form of the operators that lift the group action on the twisted sectors of a bosonic string on an orbifold , in the presence of a Kalb-Ramond field strength . These operators turn out to generate the quasi-quantum group , introduced in the context of orbifold conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche. The 3-cocycle entering in the definition of is related to by a series of cohomological equations in a tricomplex combining de Rham, Cech and group coboundaries. We construct magnetic amplitudes for the twisted sectors and show that arises as a consistency condition for the orbifold theory. Finally, we recover discrete torsion as an ambiguity in the lift of the group action to twisted sectors, in accordance with previous results presented by E. Sharpe
On a Classification of Irreducible Almost-Commutative Geometries V
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
Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets
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
The Inverse Seesaw Mechanism in Noncommutative Geometry
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
A reconstruction theorem for almost-commutative spectral triples
We propose an expansion of the definition of almost-commutative spectral
triple that accommodates non-trivial fibrations and is stable under inner
fluctuation of the metric, and then prove a reconstruction theorem for
almost-commutative spectral triples under this definition as a simple
consequence of Connes's reconstruction theorem for commutative spectral
triples. Along the way, we weaken the orientability hypothesis in the
reconstruction theorem for commutative spectral triples, and following
Chakraborty and Mathai, prove a number of results concerning the stability of
properties of spectral triples under suitable perturbation of the Dirac
operator.Comment: AMS-LaTeX, 19 pp. V4: Updated version incorporating the erratum of
June 2012, correcting the weak orientability axiom in the definition of
commutative spectral triple, stengthening Lemma A.10 to cover the
odd-dimensional case and the proof of Corollary 2.19 to accommodate the
corrected weak orientability axio
Almost-Commutative Geometries Beyond the Standard Model II: New Colours
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.Comment: Revised version for publication in J.Phys.A with corrected Higgs
masse
Almost-Commutative Geometries Beyond the Standard Model
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
Particle Physics from Almost Commutative Spacetimes
Our aim in this review article is to present the applications of Connes'
noncommutative geometry to elementary particle physics. Whereas the existing
literature is mostly focused on a mathematical audience, in this article we
introduce the ideas and concepts from noncommutative geometry using physicists'
terminology, gearing towards the predictions that can be derived from the
noncommutative description. Focusing on a light package of noncommutative
geometry (so-called 'almost commutative manifolds'), we shall introduce in
steps: electrodynamics, the electroweak model, culminating in the full Standard
Model. We hope that our approach helps in understanding the role noncommutative
geometry could play in describing particle physics models, eventually unifying
them with Einstein's (geometrical) theory of gravity.Comment: 104 pages, 5 figures, version 2 (minor changes and some additional
references
Cosmic UHE Neutrino Signatures
Utilizing the unique and reliable ultrasmall-- predictions of the
dynamical (radiative) parton model, nominal event rates and their detailed
energy dependence caused by a variety of cosmic UHE neutrino fluxes are
calculated and analyzed. In addition, maximal Regge--model inspired small--
structure functions are employed for obtaining optimal rates which do not
necessarily require `new' physics interpretations. Upward event
rates are estimated by taking into account total and nadir--angle dependent
regeneration effects due to neutral current interactions. For exploring
extragalactic neutrino sources at highest energies
(\raisebox{-0.1cm}{} GeV) with modern (future)
ground--level telescopes, we analyze horizontal air shower event rates and
shower events caused by Earth--skimming tau--neutrinos, in particular their
detailed shower-- and cosmic neutrino--energy dependence. As an illustration of
`new physics' implications we estimate the relevant horizontal air shower event
rates due to spin--2 Kaluza--Klein `graviton' exchanges in neutral current
neutrino--quark and neutrino--gluon interactions at low TeV--scales.Comment: 3 figures changed, discussions and references adde