4,449 research outputs found
Physical models from noncommutative causality
We introduced few years ago a new notion of causality for noncommutative
spacetimes directly related to the Dirac operator and the concept of Lorentzian
spectral triple. In this paper, we review in a non-technical way the
noncommutative causal structure of many toy models as almost commutative
spacetimes and the Moyal-Weyl spacetime. We show that those models present some
unexpected physical interpretations as a geometrical explanation of the
Zitterbewegung trembling motion of a fermion as well as some geometrical
constraints on translations and energy jumps of wave packets on the Moyal
spacetime.Comment: 10 pages, 4 figures, proceedings of ICNFP 201
Global Eikonal Condition for Lorentzian Distance Function in Noncommutative Geometry
Connes' noncommutative Riemannian distance formula is constructed in two
steps, the first one being the construction of a path-independent geometrical
functional using a global constraint on continuous functions. This paper
generalizes this first step to Lorentzian geometry. We show that, in a globally
hyperbolic spacetime, a single global timelike eikonal condition is sufficient
to construct a path-independent Lorentzian distance function.Comment: Special Issue on Noncommutative Spaces and Fiel
Towards a noncommutative version of Gravitation
Alain Connes' noncommutative theory led to an interesting model including
both Standard Model of particle physics and Euclidean Gravity. Nevertheless, an
hyperbolic version of the gravitational part would be necessary to make
physical predictions, but it is still under research. We shall present the
difficulties to generalize the model from Riemannian to Lorentzian Geometry and
discuss key ideas and current attempts.Comment: 7 pages, to appear in the AIP proceedings of the "Invisible Universe
International Conference", UNESCO-Paris, June 29-July 3, 200
Temporal Lorentzian Spectral Triples
We present the notion of temporal Lorentzian spectral triple which is an
extension of the notion of pseudo-Riemannian spectral triple with a way to
ensure that the signature of the metric is Lorentzian. A temporal Lorentzian
spectral triple corresponds to a specific 3+1 decomposition of a possibly
noncommutative Lorentzian space. This structure introduces a notion of global
time in noncommutative geometry. As an example, we construct a temporal
Lorentzian spectral triple over a Moyal--Minkowski spacetime. We show that,
when time is commutative, the algebra can be extended to unbounded elements.
Using such an extension, it is possible to define a Lorentzian distance formula
between pure states with a well-defined noncommutative formulation.Comment: 25 pages, a proposition has been added (Prop. 11) concerning the
recovering of the Lorentzian signature, final versio
An algebraic formulation of causality for noncommutative geometry
We propose an algebraic formulation of the notion of causality for spectral
triples corresponding to globally hyperbolic manifolds with a well defined
noncommutative generalization. The causality is given by a specific cone of
Hermitian elements respecting an algebraic condition based on the Dirac
operator and a fundamental symmetry. We prove that in the commutative case the
usual notion of causality is recovered. We show that, when the dimension of the
manifold is even, the result can be extended in order to have an algebraic
constraint suitable for a Lorentzian distance formula.Comment: 24 pages, minor changes from v2, to appear in Classical and Quantum
Gravit
Causality in noncommutative two-sheeted space-times
We investigate the causal structure of two-sheeted space-times using the
tools of Lorentzian spectral triples. We show that the noncommutative geometry
of these spaces allows for causal relations between the two sheets. The
computation is given in details when the sheet is a 2- or 4-dimensional
globally hyperbolic spin manifold. The conclusions are then generalised to a
point-dependent distance between the two sheets resulting from the fluctuations
of the Dirac operator.Comment: 26 pages, 2 figure
Noncommutative geometry, Lorentzian structures and causality
The theory of noncommutative geometry provides an interesting mathematical
background for developing new physical models. In particular, it allows one to
describe the classical Standard Model coupled to Euclidean gravity. However,
noncommutative geometry has mainly been developed using the Euclidean
signature, and the typical Lorentzian aspects of space-time, the causal
structure in particular, are not taken into account. We present an extension of
noncommutative geometry \`a la Connes suitable the for accommodation of
Lorentzian structures. In this context, we show that it is possible to recover
the notion of causality from purely algebraic data. We explore the causal
structure of a simple toy model based on an almost commutative geometry and we
show that the coupling between the space-time and an internal noncommutative
space establishes a new `speed of light constraint'.Comment: 24 pages, review article. in `Mathematical Structures of the
Universe', eds. M. Eckstein, M. Heller, S.J. Szybka, CCPress 201
Metrics and causality on Moyal planes
Metrics structures stemming from the Connes distance promote Moyal planes to
the status of quantum metric spaces. We discuss this aspect in the light of
recent developments, emphasizing the role of Moyal planes as representative
examples of a recently introduced notion of quantum (noncommutative) locally
compact space. We move then to the framework of Lorentzian noncommutative
geometry and we examine the possibility of defining a notion of causality on
Moyal plane, which is somewhat controversial in the area of mathematical
physics. We show the actual existence of causal relations between the elements
of a particular class of pure (coherent) states on Moyal plane with related
causal structure similar to the one of the usual Minkowski space, up to the
notion of locality.Comment: 33 pages. Improved version; a summary added at the end of the
introduction, misprints corrected. Version to appear in Contemporary
Mathematic
Covid-19 Belgium: Extended SEIR-QD model with nursing homes and long-term scenarios-based forecasts
We model the evolution of the covid-19 epidemic in Belgium with an
age-structured extended SEIR-QD epidemic model with separated consideration for
nursing homes. All parameters of the model are estimated using a MCMC method,
except integrated data on social contacts. The model is calibrated on
hospitals' data, number of deaths, nursing homes' tests and serological tests.
We present the current situation in November 2020 as well as long-term
scenarios-based forecasts concerning the second wave and subsequent lifting of
measures.Comment: 20 pages, 13 figures, revised presentation. Updated version of the
model with estimation of reimportations from travellers during the holidays
period. New calibration and forecasts from October 31, 202
Covid-19 Belgium:Extended SEIR-QD model with nursing homes and long-term scenarios-based forecasts
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