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Nonlinear deformations of su(2) and su(1,1) generalizing Witten's algebra

par Delbecq, Christophe ;Quesne, Christiane
Référence Journal of Physics A: Mathematical and General, 26, 4, page (L127-L134), 001
Publication Publié, 1993

Article révisé par les pairs

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Résumé :

Nonlinear deformations of su(2) and su(1,1) involving two deforming functions f(J0) and g(J0) are considered. For g(J 0)=1, they reduce to some algebras first studied by Polychronakos (1990) and Rocek (1991). Spatial emphasis is laid on the case where g(J 0) is a linear function of J0. It is shown that for any lambda =2,3,. . ., there exist ( lambda -1)-parameter algebras that are deformations of su(2) or su(1,1) respectively, and for which f(J0) is a polynomial of degree lambda . For lambda =2, such algebras are equivalent to Witten's (1990) first deformation of su(2) or su(1,1). For any lambda , the spectrum of J0 is exponential instead of linear as in the case where g(J0)=1.