Affiliation:
1. Department of Physics, Faculty of Basic Sciences, University of Guilan, Rasht 51335-1914, Iran
Abstract
In this study, we discuss a particle which is the constraint on a four-dimensional Euclidean space [Formula: see text]. In this respect and under the framework of Dirac’s approach, we analyze the classical and quantum dynamics of a particle constrained on an embedded surface in supersphere [Formula: see text], which has constant curvature and signature equal to [Formula: see text] and [Formula: see text], respectively. In fact, it is presented that the Cartesian components of momentum and position exhibit a proper description for the motion of the particle embedded in a generalized curved space. Thus, quantization of dynamics for a particle on the hypersurface [Formula: see text] derives an appropriate representation of momentum called geometric momentum as it depends on the mean curvature. The invariance algebra generated by the quantization process is an extension of [Formula: see text] with curvature parameters in both classical and quantum dynamics. Moreover, superintegrability appears in the deformed Hamiltonian [Formula: see text] arising from the Dirac brackets, in which [Formula: see text] of the underlying space behaves as the curvature (deformation) parameter.
Publisher
World Scientific Pub Co Pte Ltd
Subject
General Physics and Astronomy,Astronomy and Astrophysics,Nuclear and High Energy Physics
Cited by
1 articles.
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