19 research outputs found

    Snyder Geometry and Quantum Field Theory

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    We find that, in presence of the Snyder geometry, the notion of translational invariance needs to be modified, allowing a momentum dependence of this symmetry. This step is necessary to build the maximally localized states and the Feynman rules of the corresponding quantum field theory.Comment: 10 pages, LaTeX, no figure

    Matrix model for noncommutative gravity and gravitational instantons

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    We introduce a matrix model for noncommutative gravity, based on the gauge group U(2)U(2)U(2) \otimes U(2). The vierbein is encoded in a matrix YμY_{\mu}, having values in the coset space U(4)/(U(2)U(2))U(4)/ (U(2) \otimes U(2)), while the spin connection is encoded in a matrix XμX_\mu, having values in U(2)U(2)U(2) \otimes U(2). We show how to recover the Einstein equations from the θ0\theta \to 0 limit of the matrix model equations of motion. We stress the necessity of a metric tensor, which is a covariant representation of the gauge group in order to set up a consistent second order formalism. We finally define noncommutative gravitational instantons as generated by U(2)U(2)U(2) \otimes U(2) valued quasi-unitary operators acting on the background of the Matrix model. Some of these solutions have naturally self-dual or anti-self-dual spin connections.Comment: 28 pages, LaTeX, no figure

    Ads spacetime in Lorentz covariant gauges

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    We show how to generate the AdS spacetime metric in general Lorentz covariant gauges. In particular we propose an iterative method for solving the Lorentz gauge.Comment: 9 pages, no figure

    Remarks on the harmonic oscillator with a minimal position uncertainty.

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    We show that this problem gives rise to the same differential equation of a well known potential of ordinary quantum mechanics. However there is a subtle difference in the choice of the parameters of the hypergeometric function solving the differential equation which changes the physical discussion of the spectrum.Comment: 5 pages, no figure

    Dirac's Observables for the SU(3)XSU(2)XU(1) Standard Model

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    The complete, missing, Hamiltonian treatment of the standard SU(3)xSU(2)xU(1) model with Grassmann-valued fermion fields in the Higgs phase is given. We bypass the complications of the Hamiltonian theory in the Higgs phase, resulting from the spontaneous symmetry breaking with the Higgs mechanism, by studying the Hamiltonian formulation of the Higgs phase for the gauge equivalent Lagrangian in the unitary gauge. A canonical basis of Dirac's observables is found and the reduced physical Hamiltonian is evaluated. Its self-energy part is nonlocal for the electromagnetic and strong interactions, but local for the weak ones. Therefore, the Fermi 4-fermion interaction reappears at the nonperturbative level.Comment: 90 pages, RevTeX, no figure

    Scalar field conformally coupled to a charged black hole

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    We study the Klein-Gordon equation of a scalar field conformally coupled to a charged BTZ black hole. The background metric is obtained by coupling a non-linear and conformal invariant Maxwell field to (2+1) gravity. We show that the radial part is generally solved by a Heun function and, in the pure gravity limit, by a hypergeometric function.Comment: 9 pages, no figure