Minimal Scales from an Extended Hilbert Space

Details Minimal Scales from an Extended Hilbert Space Minimal Scales from an Extended Hilbert Space

2010-05-18

arxiv.org/abs/1005.3293v2

Class.Quant.Grav.27:245024,2010

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, version which matches that published on CQG

Scientific paper

10.1088/0264-9381/27/24/245024

We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our commutators do not depend on positions and momenta and we provide an extension of the coordinate coherent state approach to Noncommutative Geometry. We explore, as toy model, the corresponding quantum field theory in a (2+1)-dimensional spacetime. Then we investigate the more realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative planes. As a result, we obtain propagators, which are finite in the ultraviolet as well as the infrared regime.

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