12 research outputs found

    Gravitational non-commutativity and G\"odel-like spacetimes

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    We derive general conditions under which geodesics of stationary spacetimes resemble trajectories of charged particles in an electromagnetic field. For large curvatures (analogous to strong magnetic fields), the quantum mechanicical states of these particles are confined to gravitational analogs of {\it lowest Landau levels}. Furthermore, there is an effective non-commutativity between their spatial coordinates. We point out that the Som-Raychaudhuri and G\"odel spacetime and its generalisations are precisely of the above type and compute the effective non-commutativities that they induce. We show that the non-commutativity for G\"odel spacetime is identical to that on the fuzzy sphere. Finally, we show how the star product naturally emerges in Som-Raychaudhuri spacetimes.Comment: Two sections added (Relation to the fuzzy sphere, Emergence of the star product). 10 pages, Revtex. To appear in General Relativity and Gravitatio

    Poincare covariant mechanics on noncommutative space

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    The Dirac approach to constrained systems can be adapted to construct relativistic invariant theories on a noncommutative (NC) space. As an example, we propose and discuss relativistic invariant NC particle coupled to electromagnetic field by means of the standard term Aμx˙μA^\mu\dot x_\mu. Poincare invariance implies deformation of the free particle NC algebra in the interaction theory. The corresponding corrections survive in the nonrelativistic limit.Comment: 7 pages, JHEP style, final versio

    Symplectic Quantization of Open Strings and Noncommutativity in Branes

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    We show how to translate boundary conditions into constraints in the symplectic quantization method by an appropriate choice of generalized variables. This way the symplectic quantization of an open string attached to a brane in the presence of an antisymmetric background field reproduces the non commutativity of the brane coordinates.Comment: We included a comparison with previous results obtained from Dirac quantization, emphasizing the fact that in the symplectic case the boundary conditions, that lead to the non commutativity, show up from the direct application of the standard method. Version to appear in Phys. Rev.

    Geometric Quantization of Topological Gauge Theories

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    We study the symplectic quantization of Abelian gauge theories in 2+12+1 space-time dimensions with the introduction of a topological Chern-Simons term.Comment: 13 pages, plain TEX, IF/UFRJ/9

    Knot soliton in Weinberg-Salam model

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    We study numerically the topological knot solution suggested recently in the Weinberg-Salam model. Applying the SU(2) gauge invariant Abelian projection we demonstrate that the restricted part of the Weinberg-Salam Lagrangian containing the interaction of the neutral boson with the Higgs scalar can be reduced to the Ginzburg-Landau model with the hidden SU(2) symmetry. The energy of the knot composed from the neutral boson and Higgs field has been evaluated by using the variational method with a modified Ward ansatz. The obtained numerical value is 39 Tev which provides the upper bound on the electroweak knot energy.Comment: 6 pages, 3 figures, analysis of stability adde

    Time-Space Noncommutativity in Gravitational Quantum Well scenario

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    A novel approach to the analysis of the gravitational well problem from a second quantised description has been discussed. The second quantised formalism enables us to study the effect of time space noncommutativity in the gravitational well scenario which is hitherto unavailable in the literature. The corresponding first quantized theory reveals a leading order perturbation term of noncommutative origin. Latest experimental findings are used to estimate an upper bound on the time--space noncommutative parameter. Our results are found to be consistent with the order of magnitude estimations of other NC parameters reported earlier.Comment: 7 pages, revTe

    Abstract kinetic equations with positive collision operators

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    We consider "forward-backward" parabolic equations in the abstract form Jdψ/dx+Lψ=0Jd \psi / d x + L \psi = 0, 0<x<τ 0< x < \tau \leq \infty, where JJ and LL are operators in a Hilbert space HH such that J=J=J1J=J^*=J^{-1}, L=L0L=L^* \geq 0, and kerL=0\ker L = 0. The following theorem is proved: if the operator B=JLB=JL is similar to a self-adjoint operator, then associated half-range boundary problems have unique solutions. We apply this theorem to corresponding nonhomogeneous equations, to the time-independent Fokker-Plank equation μψx(x,μ)=b(μ)2ψμ2(x,μ) \mu \frac {\partial \psi}{\partial x} (x,\mu) = b(\mu) \frac {\partial^2 \psi}{\partial \mu^2} (x, \mu), 0<x<τ 0<x<\tau, μR \mu \in \R, as well as to other parabolic equations of the "forward-backward" type. The abstract kinetic equation Tdψ/dx=Aψ(x)+f(x) T d \psi/dx = - A \psi (x) + f(x), where T=TT=T^* is injective and AA satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in the introductio
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