Zernike system revisited: imaginary gauge and Higgs oscillator
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912839207223296 |
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| author | Abgaryan, Vahagn Nersessian, Armen Yeghikyan, Vahagn |
| author_facet | Abgaryan, Vahagn Nersessian, Armen Yeghikyan, Vahagn |
| contents | 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 $α,β$ parameters. When $α=2 β$ it results in the Hermitian Hamiltonian describing a free particle on (pseudo)sphere, while deviation from this point leads to a pseudo-Hermitian system. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_15713 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zernike system revisited: imaginary gauge and Higgs oscillator Abgaryan, Vahagn Nersessian, Armen Yeghikyan, Vahagn Quantum Physics Mathematical Physics Optics 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 $α,β$ parameters. When $α=2 β$ it results in the Hermitian Hamiltonian describing a free particle on (pseudo)sphere, while deviation from this point leads to a pseudo-Hermitian system. |
| title | Zernike system revisited: imaginary gauge and Higgs oscillator |
| topic | Quantum Physics Mathematical Physics Optics |
| url | https://arxiv.org/abs/2504.15713 |