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

We study complexified Harmonic Oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga [4] 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 [4] 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 Cryptooscillator in different dimensions are revealed. We also quantize the two dimensional Crypto-oscillator. E-mail:subir [email protected] E-mail: [email protected]