Localization at threshold in noncommutative space

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dc.creatorGiri, Pulak Ranjan
dc.date2008-01-02
dc.date2008-02-07
dc.date.accessioned2026-07-07T11:54:56Z
dc.date.available2026-07-07T11:54:56Z
dc.descriptionThe ground state energy of a scale symmetric system usually does not possess any lower bound, thus making the system quantum mechanically unstable. Self-adjointness and renormalization techniques usually provide the system a scale and thus making the ground state bounded from below. We on the other hand use noncommutative quantum mechanics and exploit the noncommutative parameter Θas a scale for a scale symmetric system. The resulting Hamiltonian for the system then allows an unusual bound state at the threshold of the energy, E=0. Apart from the Hamiltonian \hat{H} we also compute the other two generators of the so(2,1) algebra, the dilation \hat{D} and the conformal generator \hat{K} in the noncommutative space. The so(2,1) algebra is not closed in the noncommutative space, but the limit Θ\to 0 smoothly goes to the so(2,1) algebra restoring the conformal symmetry. We also discuss the system for large noncommutative parameter.
dc.description4 pages, no figure, Refs. added
dc.identifierhttps://arxiv.org/abs/0801.0356
dc.identifierhttp://arxiv.org/abs/0801.0356
dc.identifierPhys.Lett.A372:5123-5125,2008
dc.identifierdoi:10.1016/j.physleta.2008.06.001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/205088
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleLocalization at threshold in noncommutative space
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