Deformed Heisenberg algebras, a Fock-space representation and the Calogero model

Details Deformed Heisenberg algebras, a Fock-space representation and the Calogero model Deformed Heisenberg algebras, a Fock-space representation and the Calogero model

2000-09-13

arxiv.org/abs/hep-th/0009099v1

Eur.Phys.J.C17:539-547,2000

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, to appear in Eur. Phys. J. C

Scientific paper

10.1007/s100520000457

We describe generally deformed Heisenberg algebras in one dimension. The condition for a generalized Leibniz rule is obtained and solved. We analyze conditions under which deformed quantum-mechanical problems have a Fock-space representation. One solution of these conditions leads to a q-deformed oscillator already studied by Lorek et al., and reduces to the harmonic oscillator only in the infinite-momentum frame. The other solution leads to the Calogero model in ordinary quantum mechanics, but reduces to the harmonic oscillator in the absence of deformation.

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