Comments on dihedral and supersymmetric extensions of a family of Hamiltonians on a plane

Abstract

For any odd $k$, a connection is established between the dihedral and supersymmetric extensions of the Tremblay-Turbiner-Winternitz Hamiltonians $H_k$ on a plane. For this purpose, the elements of the dihedral group $D_{2k}$ are realized in terms of two independent pairs of fermionic creation and annihilation operators and some interesting trigonometric identities are demonstrated.

10 pages, no figure, acknowledgments added, references completed, published version

References in corpus (1)

• Calogero models and nonlocal conformal transformations

Cited by in corpus (1)

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