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arXiv · 2504.15713

Zernike system revisited: imaginary gauge and Higgs oscillator

Vahagn Abgaryan·Armen Nersessian·Vahagn Yeghikyan
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Abstract

We analyze that recently proposed clasical/quantum mechanical interpretation of Zernike system and establish its equivalence to the Higgs oscillator on sphere or pseudosphere (Lobachevsky plane). We show that the non-reality of the classical Zernike Hamiltonian is an insignificant artifact of imaginary gauge and can be eliminated with a canonical transformation. The quantum counterpart of this canonical transformation is a similarity transformation mapping the system to the quantum Higgs oscillator with integration measure depending on $\alpha,\beta$ parameters. When $\alpha=2 \beta$ it results in the Hermitian Hamiltonian describing a free particle on (pseudo)sphere, while deviation from this point leads to a pseudo-Hermitian system.

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Vahagn Abgaryan, Armen Nersessian, Vahagn Yeghikyan. 2025-04-22. Zernike system revisited: imaginary gauge and Higgs oscillator. https://arxiv.org/abs/2504.15713

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