Local currents for a deformed algebra of quantum mechanics with a fundamental length scale

TY - JOUR

T1 - Local currents for a deformed algebra of quantum mechanics with a fundamental length scale

AU - Goldin, Gerald A.

AU - Sarkar, Sarben

PY - 2006/3/17

Y1 - 2006/3/17

N2 - We explore some explicit representations of a certain stable deformed algebra of quantum mechanics, considered by R Vilela Mendes, having a fundamental length scale. The relation of the irreducible representations of the deformed algebra to those of the (limiting) Heisenberg algebra is discussed, and we construct the generalized harmonic oscillator Hamiltonian in this framework. To obtain local currents for this algebra, we extend the usual nonrelativistic local current algebra of vector fields and the corresponding group of diffeomorphisms, modelling the quantum configuration space as a commutative spatial manifold with one additional dimension.

AB - We explore some explicit representations of a certain stable deformed algebra of quantum mechanics, considered by R Vilela Mendes, having a fundamental length scale. The relation of the irreducible representations of the deformed algebra to those of the (limiting) Heisenberg algebra is discussed, and we construct the generalized harmonic oscillator Hamiltonian in this framework. To obtain local currents for this algebra, we extend the usual nonrelativistic local current algebra of vector fields and the corresponding group of diffeomorphisms, modelling the quantum configuration space as a commutative spatial manifold with one additional dimension.

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U2 - https://doi.org/10.1088/0305-4470/39/11/012

DO - https://doi.org/10.1088/0305-4470/39/11/012

M3 - Article

SN - 0305-4470

VL - 39

SP - 2757

EP - 2772

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 11

ER -