Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-04-02
Physics
High Energy Physics
High Energy Physics - Theory
based on a talk given in Second Workshop on Quantum Gravity and Noncommutative Geometry, 22nd-24th September 2008, Universidad
Scientific paper
We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, $\theta$ and $\eta$. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.
Bastos Catarina
Bertolami Orfeu
Dias Nuno
Prata Joao Nuno
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