Quantum algebraic symmetries in atomic clusters, molecules and nuclei

Details Quantum algebraic symmetries in atomic clusters, molecules and nuclei Quantum algebraic symmetries in atomic clusters, molecules and nuclei

2001-05-29

arxiv.org/abs/quant-ph/0105143v1

Condensed Matter Theor. 15 (2000) 25

Physics

Quantum Physics

Plain TeX, 10 pages. Lecture given at the XXIII International Workshop on Condensed Matter Theories (Ithaca, Greece, 17-23/6/1

Scientific paper

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.

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