Polynomial Lie Algebras $sl_{pd}(2)$ in Action: Smooth $sl(2)$ Mappings and Approximations

Details Polynomial Lie Algebras $sl_{pd}(2)$ in Action: Smooth $sl(2)$ Mappings and Approximations Polynomial Lie Algebras $sl_{pd}(2)$ in Action: Smooth $sl(2)$ Mappings and Approximations

1995-12-09

arxiv.org/abs/quant-ph/9512010v1

Physics

Quantum Physics

8 pages, LATEX

Scientific paper

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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