Geometric models of (d+1)-dimensional relativistic rotating oscillators
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چکیده
Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the energy levels and corresponding normalized energy eigenfunctions. An important property is that all these models have the same nonrelativistic limit, namely the usual harmonic oscillator. Pacs 04.62.+v In general relativity the anti-de Sitter (AdS) spacetime is one of the most important and interesting pieces since the AdS/Conformal field theorycorrespondence [1] has been discovered. It is known that, because of the high symmetry of AdS, the free motion of the scalar classical or quantum particles on this background has special features. There is a local chart with a metric [2] able to reproduce the classical motion of an isotropic nonrelativistic harmonic oscillator (NRHO). In other respects, the energy levels of the quantum modes given by the Klein-Gordon equation are equidistant [3]. Thus the geometric models of free test classical or quantum particles on AdS backgrounds represent the relativistic correspondent of the NRHO. Two years ago, we have generalized this ideal model of relativistic oscillator (RO) to new families of models of RO in (1+1) and (3+1) dimensions
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تاریخ انتشار 2008