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Paper   IPM / Physic / 8399
School of Physics
  Title:   Beyond Unitary Parasupersymmetry from the Viewpoint of h3 and h4 Heisenberg Algebras
1.  A. Chenaghlou
2.  H. Fakhri
  Status:   Published
  Journal: Mod. Phys. Lett. A
  No.:  30
  Vol.:  20
  Year:  2006
  Pages:   2303-2312
  Supported by:  IPM
Using the partition of the number p−1 into p−1 real parts which are not equal with each other necessarily, we develop the unitary parasupersymmetry algebra of arbitrary order p so that the well-known RubakovSpiridonovKhare parasupersymmetry becomes a special case of the developed one. It is shown that the developed algebra is realized by simple harmonic oscillator and Landau problem on a at surface with the symmetries of h3 and h4 HeisenbergLie algebras. For this new parasupersymmetry, the well-known unitary condition is violated, however, unitarity of the corresponding algebra is struc- turally conserved. Moreover, the components of the bosonic Hamiltonian operator are derived as functions from the mean value of the partition numbers with their label weight function.

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