Abstract
Quantum analogues of the limiting symmetries U(1) and O(2) of the U(2) algebra are studied. In particular, the authors have investigated the question whether the q-deformation parameter in the algebra of the SU(2)q group can be looked upon as a dynamical symmetry breaking parameter taking one from one limiting case to another. They find that in the limiting case of U(2) contains/implies U(1), partially the real and imaginary q-deformations and more completely the complex q-deformations can take one not only from U(1) towards O(2) but also give intermediate results. The role of complex quantum deformations is analysed for the first time. Also, the possible consequences of this work for nuclei and molecules are discussed.
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