q-Deformed Weyl Superalgebra

Let s and t be two positive integers. The Weyl superalgebra , denoted by W(s, t), is generated by the annihilation and creation operators of s Bose and t Fermi oscillators . The q-deformation W _q (s, t) of W(s, t) is obtained by introducing the quantum analogues of these oscillators. [1]

The annihilation, creation and number operators b _i , and N _i , i = 1,..., s, of bosonic q-oscillators are taken to satisfy,

and for i ≠ j

with parity p(b _i ) = p = p(N _i ) = 0.

Similarly, the annihilation, creation and number operators, Ψ _i , and M _i , i = 1,..., t, of fermionic q-oscillators are defined through

and for i ≠ j,

with p(Ψ _i ) = p() = 1, p(M _i ) = 0, and {x, y} = xy + yx. It is further assumed that bosonic and fermionic operators commute,

The algebra W _q (s, t) generated by the operators b _i , , N _i , i = 1,..., s, and Ψ _j , , M _j , j = 1,..., t, subjected to above conditions, is referred to as q-analogue of the...