Crypto-Harmonic Oscillator in Higher Dimensions: Classical and Quantum Aspects
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We study complexified Harmonic Oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga \cite{sm} who initiated the study of these Crypto-gauge invariant models that can be related to $PT$-symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints, (in contrast to \cite{sm} where one deals with a single constraint), with a much richer constraint structure. Some common as well as distinct features in the study of the same Crypto-oscillator in different dimensions are revealed. We also quantize the two dimensional Crypto-oscillator.
17 pages, Latex, enlarges version, added ref.s., accepted in J.Phys.A, slight alteration in reference section and text, matches journal version
17 pages, Latex, enlarges version, added ref.s., accepted in J.Phys.A, slight alteration in reference section and text, matches journal version