Abstract
The use of spectrum generating algebras in the description of the nuclear many-body system is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced with the help of simple examples. It is then indicated how techniques based on symmetry considerations can be used to find the analytical solutions for the problem of an aggregate of interacting particles (bosons and/or fermions). Some older ideas due to Wigner, Racah and Elliott are succinctly summarized to put more recent advances in a proper perspective. It is then shown that similar techniques are used in a model of the nucleus in terms of interacting bosons due to Arima and Iachello. Subsequent extensions of this model to odd-mass nuclei lead to the consideration of mixed systems of bosons and fermions and, most notably, to supersymmetry.
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