# Noncommutative Quantum Mechanics and Quantum Cosmology - High Energy Physics - Theory

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Abstract: We present a phase-space noncommutative version of quantum mechanics andapply this extension to Quantum Cosmology. We motivate this type ofnoncommutative algebra through the gravitational quantum well GQW where thenoncommutativity between momenta is shown to be relevant. We also discuss somequalitative features of the GQW such as the Berry phase. In the context ofquantum cosmology we consider a Kantowski-Sachs cosmological model and obtainthe Wheeler-DeWitt WDW equation for the noncommutative system through the ADMformalism and a suitable Seiberg-Witten SW map. The WDW equation isexplicitly dependent on the noncommutative parameters, $\theta$ and $\eta$. Weobtain numerical solutions of the noncommutative WDW equation for differentvalues of the noncommutative parameters. We conclude that the noncommutativityin the momenta sector leads to a damped wave function implying that this typeof noncommmutativity can be relevant for a selection of possible initial statesfor the universe.

Autor: Catarina Bastos, Orfeu Bertolami, Nuno Dias, Joao Nuno Prata

Fuente: https://arxiv.org/