The Para-Bose oscillator in a finite linear space

B. Mojaveri, Alireza Dehghani, R. Jafarzadeh Bahrbeig

Fethi Bouzeffour, Hanen Ben Mansour

Ha Huy Bang

R. J. Cova

In the Fock space of two Bose operators all the irreducible representations of both the 1-D para-Bose and para-Fermi oscillators are constructed. Bose states of the form |p + k–1, kn > (|p – k, kn), n = 1,2, are shown to stand for states of k-parabosons (k-parafermions) of order p. For n = 1 or n = 2 the various subspaces may be visualized in the plane as either straight-lines or parabolae, respectively.

S. Chaturvedi, Venkatraman Srinivasan

We show that a single para-Bose oscillator may be regarded as a deformed Bose oscillator. We construct a nonlinear realization of the single-mode para-Bose algebra in terms of a single boson. This is in contrast to the Green decomposition that expresses a single para-Bose oscillator in terms of p anticommuting bosons. We also construct an operator canonically conjugate to the para-Bose annihilation operator that permits us to carry over familiar constructions to the para-Bosonic case.