1,720,990 research outputs found
On Twisting Real Spectral Triples by Algebra Automorphisms
No full textOn the configuration space of projections in a noncommutative algebra, and for an automorphism of the algebra, we use a twisted Hochschild cocycle for an action functional, and a twisted cyclic cocycle for a topological term. The latter is Hochschild-cohomologous to the former and positivity in twisted Hochschild cohomology results into a lower bound for the action functional. While the equations for the critical points are rather complicate, the use of the positivity and the bound by the topological term leads to self-duality equations (thus yielding twisted noncommutative sigma-model solitons, or instantons). We present explicit non trivial solutions on the quantum projective line
CONFORMAL MAPPING OF UNRUH TEMPERATURE
No full textIn the framework of conformal field theory, the mapping from (unbounded) wedge regions of Minkowski space time to (bounded) double-cone regions is extended to the Unruh temperature associated to a uniformly accelerated observer. The link between a previous result, the diamond's temperature, and the conformal factor (Weyl rescaling of the metric) is worked out. One thus explains from a mathematical point of view why an observer with finite lifetime experiences the vacuum as a thermal state whatever his acceleration, even vanishing.EU [EIF025947-QGNC
LINE LEMENT IN QUANTUM GRAVITY: THE EXAMPLE OF DSR AND NONCOMMUTATIVE GEOMETRY
No full textWe question the notion of line element in some quantum spaces that are expected to play a role in quantum gravity, namely noncommutative deformations of Minkowski spaces. We recall how the implementation of the Leibniz rule for bids to see some of the infinitesimal deformed Poincare transformations as good candidates for Noether symmetries. Then were call the more fundamental view on the line element proposed in noncommutative geometry,and re-interprete at this light some previous results on Connes' distance formula
Connes distance and optimal transport
No full textWe give a brief overview on the relation between Connes spectral distance in noncommutative geometry and the Wasserstein distance of order 1 in optimal transport. We first recall how these two distances coincide on the space of probability measures on a Riemannian manifold. Then we work out a simple example on a discrete space, showing that the spectral distance between arbitrary states does not coincide with the Wasserstein distance with cost the spectral distance between pure states
A critical survey of twisted spectral triples beyond the Standard Model
Full text linkWe review the applications of twisted spectral triples to the Standard Model.
The initial motivation was to generate a scalar field, required to stabilise
the electroweak vacuum and fit the Higgs mass, while respecting the first-order
condition. Ultimately, it turns out that the truest interest of the twist lies
in a new -- and unexpected -- field of 1-forms, which is related to the
transition from Euclidean to Lorentzian signature.Comment: Published versions. Minor misprints and acknowledgments update
Beyond the Standard Model with noncommutative geometry, strolling towards quantum gravity
No full textNoncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: from models of quantum spacetime(with or without breaking of Lorentz symmetry) to loop gravity and string theory, from early considerations on UV-divergenciesin quantum field theory to recent models of gauge theories on noncommutatives pacetime, from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. We list several of these applications, emphasizing also the original point of view brought by noncommutative geometry on the nature of time. This text serves as an introduction to the volume of proceedings of the parallel session "Noncommutative geometry and quantum gravity", as a part of the conference "Conceptual and technical challenges in quantum gravity" organized at the University of Rome La Sapienza sin September 2014
Grand symmetry, spectral action and the Higgs mass
Full text linkIn the context of the spectral action and the noncommutative geometry approach to the standard model, we build a model based on a larger symmetry. With this grand symmetry it is natural to have the scalar field necessary to obtain the Higgs mass in the vicinity of 126 GeV. This larger symmetry mixes gauge and spin degrees of freedom without introducing extra fermions. Requiring the noncommutative space to be an almost commutative geometry (i.e. the product of manifold by a finite dimensional internal space) gives conditions for the breaking of this grand symmetry to the standard model
Designing the sound of a cut-off drum
No full textThe spectral action in noncommutative geometry naturally implements an ultraviolet cut-off, bycounting the eigenvalues of a (generalized) Dirac operator lower than an energy of unification.Inverting the well known question “how to hear the shape of a drum”, we ask what drum can bedesigned by hearing the truncated music of the spectral action ? This makes sense because thesame Dirac operator also determines the metric, via Connes distance. The latter thus offers anoriginal way to implement the high-momentum cut-off of the spectral action as a short distancecut-off on space. This is a non-technical presentation of the results of
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