1,720,983 research outputs found
Is life a thermal horizon?
No full textThis talk aims at questioning the vanishing of Unruh temperature for an inertial observer in Minkovski spacetime with finite lifetime, arguing that in the non eternal case the existence of a causal horizon is not linked to the non-vanishing of the acceleration. This is illustrated by a previous result, the diamonds temperature, that adapts the algebraic approach of Unruh effect to the finite case
What kind of noncommutative geometry for quantum gravity?
No full textWe give a brief account of the description of the standard model in noncommutative geometry as well as the thermal time hypothesis, questioning their relevance for quantum gravity
Line element 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
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
Towards a Monge − Kantorovich Metric in Noncommutative Geometry
No full textWe investigate whether the identification between Cannes' spectral distance in noncommutative geometry and the Monge-Kantorovich distance of order 1 in the theory of optimal transport - which has been pointed out by Rieffel in the commutative case - still makes sense in a noncommutative framework. To this aim, given a spectral triple (A, H, D) with noncommutative A, we introduce a "Monge Kantorovich"-like distance WDon the space of states of A, taking as a cost function the spectral distance dDbetween, pure states. We show in full generality that dD⤠WD, and exhibit several examples where the equality actually holds true, in particular, on the unit two-ball viewed as the state space of M2(â). We also discuss WDin a two-sheet model (the product of a manifold and â2), pointing towards a possible interpretation of the Higgs field as a cost function that does not vanish, on, the diagonal. Bibliography: 48 titles. © 2014 Springer Science+Business Media New York
Spectral distance on the circle
No full textAbstractA building block of non-commutative geometry is the observation that most of the geometric information of a compact Riemannian spin manifold M is encoded within its Dirac operator D. Especially via Connes' distance formula one is able to extract from the spectral properties of D the geodesic distance on M. In this paper we investigate the distance d encoded within a covariant Dirac operator on a trivial U(n)-fiber bundle over the circle with arbitrary connection. It turns out that the connected components of d are tori whose dimension is given by the holonomy of the connection. For n=2 we explicitly compute d on all the connected components. For n⩾2 we restrict to a given fiber and find that the distance is given by the trace of the module of a matrix. The latest is defined by the holonomy and the coordinate of the points under consideration. This paper extends to arbitrary n and arbitrary connection the results obtained in a previous work for U(2)-bundle with constant connection. It confirms interesting properties of the spectral distance with respect to another distance naturally associated to connection, namely the horizontal or Carnot–Carathéodory distance dH. Especially in case the connection has irrational components, the connected components for d are the closure of the connected components of dH within the Euclidean topology on the torus
Noncommutative Geometry of the Moyal Plane: Translation Isometries, Connes' Distance on Coherent States, Pythagoras Equality
No full textWe study the metric aspect of the Moyal plane from Connes' noncommutative geometry point of view. First, we compute Connes' spectral distance associated with the natural isometric action of on the algebra of the Moyal plane . We show that the distance between any state of and any of its translated states is precisely the amplitude of the translation. As a consequence, we obtain the spectral distance between coherent states of the quantum harmonic oscillator as the Euclidean distance on the plane. We investigate the classical limit, showing that the set of coherent states equipped with Connes' spectral distance tends towards the Euclidean plane as the parameter of deformation goes to zero. The extension of these results to the action of the symplectic group is also discussed, with particular emphasis on the orbits of coherent states under rotations. Second, we compute the spectral distance in the double Moyal plane, intended as the product of (the minimal unitization of) by . We show that on the set of states obtained by translation of an arbitrary state of , this distance is given by the Pythagoras theorem. On the way, we prove some Pythagoras inequalities for the product of arbitrary unital and non-degenerate spectral triples. Applied to the Doplicher- Fredenhagen-Roberts model of quantum spacetime [DFR], these two theorems show that Connes' spectral distance and the DFR quantum length coincide on the set of states of optimal localization
Noncommutative gauge theories on Rθ2 as matrix models
No full textWe study a class of noncommutative gauge theory models on 2-dimensional Moyal space from the viewpoint of matrix models and explore some related properties. Expanding the action around symmetric vacua generates non local matrix models with polynomial interaction terms. For a particular vacuum, we can invert the kinetic operator which is related to a Jacobi operator. The resulting propagator can be expressed in terms of Chebyschev polynomials of second kind. We show that non vanishing correlations exist at large separations. General considerations on the kinetic operators stemming from the other class of symmetric vacua, indicate that only one class of symmetric vacua should lead to fast decaying propagators. The quantum stability of the vacuum is briefly discussed. © 2013 SISSA
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