Effective action for noncommutative Bianchi I model

Journal Article · Wed Jun 12 04:00:00 EDT 2013 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4810779· OSTI ID:22118574

Rosenbaum, M.; Vergara, J. D. ^[1]; Minzoni, A. A. ^[2]

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1. Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico 04510 DF (Mexico)
2. FENOMEC-IIMAS, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico 04510 DF (Mexico)

Quantum Mechanics, as a mini-superspace of Field Theory has been assumed to provide physically relevant information on quantum processes in Field Theory. In the case of Quantum Gravity this would imply using Cosmological models to investigate quantum processes at distances of the order of the Planck scale. However because of the Stone-von Neuman Theorem, it is well known that quantization of Cosmological models by the Wheeler-DeWitt procedure in the context of a Heisenberg-Weyl group with piecewise continuous parameters leads irremediably to a volume singularity. In order to avoid this information catastrophe it has been suggested recently the need to introduce in an effective theory of the quantization some form of reticulation in 3-space. On the other hand, since in the geometry of the General Relativistic formulation of Gravitation space can not be visualized as some underlying static manifold in which the physical system evolves, it would be interesting to investigate whether the effective reticulation which removes the singularity in such simple cosmologies as the Bianchi models has a dynamical origin manifested by a noncommutativity of the generators of the Heisenberg-Weyl algebra, as would be expected from an operational point of view at the Planck length scale.

• OSTI ID: 22118574
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1540; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

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GEOMETRY
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