dorsal/arxiv
View SchemaPolynomial Lie Algebras $sl_{pd}(2)$ in Action: Smooth $sl(2)$ Mappings and Approximations
| Authors | V. P. Karassiov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9512010 |
| URL | https://arxiv.org/abs/quant-ph/9512010 |
Abstract
We examine applications of polynomial Lie algebras $sl_{pd}(2)$ to solve physical tasks in $G_{inv}$-invariant models of coupled subsystems in quantum physics. A general operator formalism is given to solve spectral problems using expansions of generalized coherent states, eigenfunctions and other physically important quantities by power series in the $sl_{pd}(2)$ coset generators $V_{\pm}$. We also discuss some mappings and approximations related to the familiar $sl(2)$ algebra formalism. On this way a new closed analytical expression is found for energy spectra which coincides with exact solutions in certain cases and, in general, manifests an availability of incommensurable eigenfrequencies related to a nearly chaotic dynamics of systems under study.
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"date_created": "2026-03-02T18:02:38.023000Z",
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"abstract": "We examine applications of polynomial Lie algebras $sl_{pd}(2)$ to solve\nphysical tasks in $G_{inv}$-invariant models of coupled subsystems in quantum\nphysics. A general operator formalism is given to solve spectral problems using\nexpansions of generalized coherent states, eigenfunctions and other physically\nimportant quantities by power series in the $sl_{pd}(2)$ coset generators\n$V_{\\pm}$. We also discuss some mappings and approximations related to the\nfamiliar $sl(2)$ algebra formalism. On this way a new closed analytical\nexpression is found for energy spectra which coincides with exact solutions in\ncertain cases and, in general, manifests an availability of incommensurable\neigenfrequencies related to a nearly chaotic dynamics of systems under study.",
"arxiv_id": "quant-ph/9512010",
"authors": [
"V. P. Karassiov"
],
"categories": [
"quant-ph"
],
"title": "Polynomial Lie Algebras $sl_{pd}(2)$ in Action: Smooth $sl(2)$ Mappings and Approximations",
"url": "https://arxiv.org/abs/quant-ph/9512010"
},
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