NONCOMMUTATIVE QUANTUM MECHANICS AND QUANTUM COSMOLOGY

• Type: Article in International Scientific Journal
• Date: 2009

Authors

Catarina Bastos (Author) Other; Orfeu Bertolami (Author) Other; Nuno Costa Dias (Author) Other; Joao Nuno Prata (Author) Other

Journal

Title: International Journal of Modern Physics A

Vol. 24

Pages: 2741-2752

ISSN: 0217-751X

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 24 Citations

Scopus - 26 Citations

Scientific classification

FOS: Natural sciences > Physical sciences

Other information

Authenticus ID: P-003-J5D

DOI: 10.1142/s0217751x09046138

Abstract (EN): 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,. and.. 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 12