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Paper IPM / P / 6524  


Abstract:  
The (p=2) paraboseparafermi supersymmetry
is studied in general terms. It is
shown that the algebraic structure of the (p=2) parastatistical dynamical
variables allows for (symmetry) transformations which mix the parabose and
parafermi coordinate variables. The example of a simple paraboseparafermi
oscillator is discussed and its symmetries investigated. It turns out that this
oscillator possesses two paraboseparafermi supersymmetries. The combined set
of generators of the symmetries forms the algebra
of supersymmetric quantum mechanics supplemented with an additional central
charge. In this sense there is no relation between the paraboseparafermi
supersymmetry and the parasupersymmetric quantum mechanics. A precise
definition of a quantum system involving this type of paraboseparafermi
supersymmetry is offered, thus introducing (p=2) supersymmetric paraquantum
mechanics. The spectrum degneracy structure of general (p=2) supersymmetric
paraquantum mechanics is analyzed in detail. The energy
eigenvalues and eigenvectors for the paraboseparafermi oscillator are then
obtained explicitly. The latter confirms the validity of the results obtained
for general supersymmetric paraquantum mechanics.
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