5 research outputs found

    Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology

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    Using the ADM formalism in the minisuperspace, we obtain the commutative and noncommutative exact classical solutions and exact wave function to the Wheeler-DeWitt equation with an arbitrary factor ordering, for the anisotropic Bianchi type I cosmological model, coupled to a scalar field, cosmological term and barotropic perfect fluid. We introduce noncommutative scale factors, considering that all minisuperspace variables qi\rm q^i do not commute, so the symplectic structure was modified. In the classical regime, it is shown that the anisotropic parameter β±nc\rm \beta_{\pm nc} and the field ϕ\phi, for some value in the λeff\lambda_{eff} cosmological term and noncommutative θ\theta parameter, present a dynamical isotropization up to a critical cosmic time tct_{c}; after this time, the effects of isotropization in the noncommutative minisuperspace seems to disappear. In the quantum regimen, the probability density presents a new structure that corresponds to the value of the noncommutativity parameter.Comment: 17 pages, 6 figures, Acepted in IJT

    The sl(2n|2n)^(1) Super-Toda Lattices and the Heavenly Equations as Continuum Limit

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    The nn\to\infty continuum limit of super-Toda models associated with the affine sl(2n2n)(1)sl(2n|2n)^{(1)} (super)algebra series produces (2+1)(2+1)-dimensional integrable equations in the S1×R2{\bf S}^{1}\times {\bf R}^2 spacetimes. The equations of motion of the (super)Toda hierarchies depend not only on the chosen (super)algebras but also on the specific presentation of their Cartan matrices. Four distinct series of integrable hierarchies in relation with symmetric-versus-antisymmetric, null-versus-nonnull presentations of the corresponding Cartan matrices are investigated. In the continuum limit we derive four classes of integrable equations of heavenly type, generalizing the results previously obtained in the literature. The systems are manifestly N=1 supersymmetric and, for specific choices of the Cartan matrix preserving the complex structure, admit a hidden N=2 supersymmetry. The coset reduction of the (super)-heavenly equation to the I×R(2)=(S1/Z2)×R2{\bf I}\times{\bf R}^{(2)}=({\bf S}^{1}/{\bf Z}_2)\times {\bf R}^2 spacetime (with I{\bf I} a line segment) is illustrated. Finally, integrable N=2,4N=2,4 supersymmetrically extended models in (1+1)(1+1) dimensions are constructed through dimensional reduction of the previous systems.Comment: 12 page

    Noncommutative quantum mechanics and Bohm's ontological interpretation

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    We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are determined, and the implications of its adoption for noncommutativity are discussed. A Bohmian analysis of the noncommutative harmonic oscillator is carried out in detail. By studying the particle motion in the oscillator orbits, we show that small-scale physics can have influence at large scales, something similar to the IR-UV mixing
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