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

Abstract

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

References in corpus (11)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• A new PT symmetric complex Hamiltonian with a real spectra
• Pseudo-Hermiticity, weak pseudo-Hermiticity and eta-orthogonality condition
• Quantisation of $O(N)$ invariant nonlinear sigma model in the Batalin-Tyutin formalism
• A Canonical Approach to the Quantization of the Damped Harmonic Oscillator
• Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• PT symmetry of a conditionally exactly solvable potential
• Moyal products -- a new perspective on quasi-hermitian quantum mechanics
• Real Description of Classical Hamiltonian Dynamics Generated by a Complex Potential

Cited by in corpus (2)

• Pseudo-Hermitian Representation of Quantum Mechanics
• Classical oscillator with position-dependent mass in a complex domain