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Quantum algebraic symmetries in atomic clusters, molecules and nuclei
D. Bonatsos, N. Karoussos, P. P. Raychev, R. P. Roussev
abstract: Quantum algebras (also called quantum groups) are deformed versions of the
usual Lie algebras, to which they reduce when the deformation parameter q is
set equal to unity. From the mathematical point of view they are Hopf algebras.
Their use in physics became popular with the introduction of the q-deformed
harmonic oscillator as a tool for providing a boson realization of the quantum
algebra SUq(2), although similar mathematical structures had already been
known. Initially used for solving the quantum Yang-Baxter equation, quantum
algebras have subsequently found applications in several branches of physics,
as, for example, in the description of spin chains, squeezed states, hydrogen
atom and hydrogen-like spectra, rotational and vibrational nuclear and
molecular spectra, and in conformal field theories. By now much work has been
done on the q-deformed oscillator and its relativistic extensions, and several
kinds of generalized deformed oscillators and SU(2) algebras have been
introduced. Here we shall confine ourselves to a list of applications of
quantum algebras in nuclear structure physics and in molecular physics and, in
addition, a recent application of quantum algebraic techniques to the structure
of atomic clusters will be discussed in more detail.
- oai_identifier:
- oai:arXiv.org:quant-ph/0105143
- categories:
- quant-ph math-ph math.MP nucl-th physics.chem-ph
- comments:
- Plain TeX, 10 pages. Lecture given at the XXIII International
Workshop on Condensed Matter Theories (Ithaca, Greece, 17-23/6/1999)
- arxiv_id:
- quant-ph/0105143
- journal_ref:
- Condensed Matter Theor. 15 (2000) 25
- report_no:
- DEM-NT-99-13
- created:
- 2001-05-29
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