%0 Journal Article
%D 2014
%T A modular spectral triple for κ-Minkowski space
%A Marco Matassa
%X We present a spectral triple for κ-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the κ-Poincaré algebra. The weight satisfies a KMS condition and its associated modular operator plays an important role in the construction. This forces us to introduce two ingredients which have a modular flavour: the first is a twisted commutator, used to obtain a boundedness condition for the Dirac operator, and the second is a weight replacing the usual operator trace, used to measure the growth of the resolvent of the Dirac operator. We show that, under some assumptions related to the symmetries and the classical limit, there is a unique Dirac operator and automorphism such that the twisted commutator is bounded. Then, using the weight mentioned above, we compute the spectral dimension associated to the spectral triple and find that is equal to the classical dimension. Finally we briefly discuss the introduction of a real structure.
%I Elsevier
%G en
%U http://urania.sissa.it/xmlui/handle/1963/34895
%1 35180
%2 Mathematics
%4 1
%$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-04T16:52:19Z
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%R 10.1016/j.geomphys.2013.10.023
%0 Thesis
%D 2014
%T Non-commutative integration for spectral triples associated to quantum groups
%A Marco Matassa
%K Non-commutative geometry
%X This thesis is dedicated to the study of non-commutative integration, in the sense of spectral triples, for some non-commutative spaces associated to quantum groups.
%I SISSA
%G en
%1 7363
%2 Mathematics
%4 1
%# MAT/07 FISICA MATEMATICA
%$ Submitted by Marco Matassa (mmatassa@sissa.it) on 2014-04-28T08:04:56Z
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%0 Journal Article
%D 2014
%T Quantum dimension and quantum projective spaces
%A Marco Matassa
%X We show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dbrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K2por its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connection with the well known notion of quantum dimension of quantum group theory is pointed out.
%I Institute of Mathematics
%G en
%U http://urania.sissa.it/xmlui/handle/1963/34764
%1 34991
%2 Physics
%4 2
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%R 10.3842/SIGMA.2014.097
%0 Journal Article
%J Phys. Rev. D 86 (2012) 124035
%D 2012
%T Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
%A Giovanni Amelino-Camelia
%A Antonino Marciano
%A Marco Matassa
%A Giacomo Rosati
%K Doubly special relativity
%X The interest of part of the quantum-gravity community in the possibility of\r\nPlanck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangible. We here provide a significant step toward filling this gap by exhibiting an explicit example of Planck-scale-deformed relativistic symmetries of a spacetime with constant rate of expansion (deSitterian). Technically we obtain the first ever example of a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale (\"speed-of-light scale\"), a large distance scale (inverse of the \"expansion-rate scale\"), and a large momentum scale (\"Planck scale\"). We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality. We also offer a preliminary analysis of the differences between the scenario we here propose and the most studied scenario for broken (rather than deformed) Lorentz symmetry in expanding spacetimes.
%B Phys. Rev. D 86 (2012) 124035
%I American Physical Society
%G en
%1 6496
%2 Physics
%4 -1
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%R 10.1103/PhysRevD.86.124035