On the deformability of Heisenberg algebras

Details On the deformability of Heisenberg algebras On the deformability of Heisenberg algebras

1995-08-24

arxiv.org/abs/q-alg/9508014v1

Commun. Math. Phys. 180 (1996) 23

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, latex, no figures

Scientific paper

10.1007/BF02101181

Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum mechanics. For the case of a q-oscillator there exists a deforming map to the classical algebra. It is shown that the differential calculus on quantum planes with involution, i.e. if one works in position-momentum realization, can be mapped on a q-difference calculus on a commutative real space. Although this calculus leads to an interesting discretization it is proved that it can be realized by generators of the undeformed algebra and does not posess a proper group of global transformations.

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