Realizations of the Lie superalgebra q(2) and applications

Details Realizations of the Lie superalgebra q(2) and applications Realizations of the Lie superalgebra q(2) and applications

2001-04-27

arxiv.org/abs/math-ph/0104038v2

Physics

Mathematical Physics

LaTeX file, 15 pages. (further references added, minor changes in section 5)

Scientific paper

10.1088/0305-4470/34/39/311

The Lie superalgebra q(2) and its class of irreducible representations V_p of dimension 2p (p being a positive integer) are considered. The action of the q(2) generators on a basis of V_p is given explicitly, and from here two realizations of q(2) are determined. The q(2) generators are realized as differential operators in one variable x, and the basis vectors of V_p as 2-arrays of polynomials in x. Following such realizations, it is observed that the Hamiltonian of certain physical models can be written in terms of the q(2) generators. In particular, the models given here as an example are the sphaleron model, the Moszkowski model and the Jaynes-Cummings model. For each of these, it is shown how the q(2) realization of the Hamiltonian is helpful in determining the spectrum.

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