Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-09-27
J.Phys.A41:065306,2008
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, Latex, enlarges version, added ref.s., accepted in J.Phys.A, slight alteration in reference section and text, matche
Scientific paper
10.1088/1751-8113/41/6/065306
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.
Ghosh Subir
Majhi Bibhas Ranjan
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