Effective action for noncommutative Bianchi I model
Abstract
Quantum Mechanics, as a minisuperspace 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 Stonevon Neuman Theorem, it is well known that quantization of Cosmological models by the WheelerDeWitt procedure in the context of a HeisenbergWeyl 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 3space. 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 HeisenbergWeyl algebra, as would be expected from an operational point of view at the Planck length scale.
 Publication:

II CINVESTAVUNAM Symposium on High Energy Physics, Particles and Neutrinos in an Astrophysical Context: in Honor of Juan Carlos D'Olivo
 Pub Date:
 June 2013
 DOI:
 10.1063/1.4810779
 Bibcode:
 2013AIPC.1540..113R
 Keywords:

 cosmology;
 general relativity;
 noncommutative field theory;
 quantisation (quantum theory);
 quantum gravity;
 03.70.+k;
 04.60.Pp;
 11.10.Nx;
 98.80.Qc;
 Theory of quantized fields;
 Loop quantum gravity quantum geometry spin foams;
 Noncommutative field theory;
 Quantum cosmology