Zernike system revisited: imaginary gauge and Higgs oscillator

• URL: http://arxiv.org/abs/2504.15713v1
• Date: Tue, 22 Apr 2025 08:55:07 GMT
• Title: Zernike system revisited: imaginary gauge and Higgs oscillator
• Authors: Vahagn Abgaryan, Armen Nersessian, Vahagn Yeghikyan,
• Abstract summary: We show that the non-reality of the classical Zernike Hamiltonian is an insignificant artifact of imaginary gauge.<n>The quantum counterpart of this canonical transformation is a similarity transformation mapping the system to the quantum Higgs oscillator.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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