N=2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane

Details N=2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane N=2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane

2010-04-26

arxiv.org/abs/1004.4508v1

J. Phys. A 43 (2010) 305202, 12 pages

Physics

Mathematical Physics

18 pages, no figure

Scientific paper

The family of Tremblay-Turbiner-Winternitz Hamiltonians $H_k$ on a plane, corresponding to any positive real value of $k$, is shown to admit a ${\cal N} = 2$ supersymmetric extension of the same kind as that introduced by Freedman and Mende for the Calogero problem and based on an ${\rm osp}(2/2, \R) \sim {\rm su}(1,1/1)$ superalgebra. The irreducible representations of the latter are characterized by the quantum number specifying the eigenvalues of the first integral of motion $X_k$ of $H_k$. Bases for them are explicitly constructed. The ground state of each supersymmetrized Hamiltonian is shown to belong to an atypical lowest-weight state irreducible representation.

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