Chiral super-Tremblay-Turbiner-Winternitz Hamiltonians and their dynamical superalgebra

Details Chiral super-Tremblay-Turbiner-Winternitz Hamiltonians and their dynamical superalgebra Chiral super-Tremblay-Turbiner-Winternitz Hamiltonians and their dynamical superalgebra

2010-08-25

arxiv.org/abs/1008.4269v2

J.Phys.A43:495203,2010

Physics

Mathematical Physics

14 pages, no figure, published version

Scientific paper

10.1088/1751-8113/43/49/495203

The family of Tremblay-Turbiner-Winternitz (TTW) Hamiltonians $H_k$ on a plane, corresponding to any positive real value of $k$, is shown to admit another ${\cal N} = 2$ supersymmetric extension than that previously introduced by the present author. This new extension is of the same kind as that considered by D'Hoker and Vinet in the study of magnetic monopoles and is characterized by the fact that all the irreducible representations of the corresponding ${\rm osp}(2/2, \R)$ dynamical superalgebra are atypical lowest-weight state ones. The new supersymmetric Hamiltonians may be referred to as chiral super-TTW Hamiltonians, the role of chirality being played here by the fermion number parity operator.

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