Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry

Details Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry

1993-11-24

arxiv.org/abs/hep-th/9311147v1

J.Math.Phys.35:4483-4496,1994

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, Latex, preprint DAMTP/93-65

Scientific paper

10.1063/1.530798

We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the underlying noncommutative geometry, a length and a momentum scale appear, leading to the existence of minimal nonzero uncertainties in the positions and momenta. The usual quantum mechanical behaviour is recovered as a limiting case for not too small and not too large distances and momenta.

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