Crypto-Harmonic Oscillator in Higher Dimensions: Classical and Quantum Aspects

الأصل · EN

We study complexified Harmonic Oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga 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 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.