Representations of Osp(1,4) in Terms of Three Boson Pairs and Matrices of Arbitrary Even Order. Description of the Method

摘要

Two-parameter family of infinite-dimensional Schur-irreducible representations of the Lie superalgebra osp (1, 4) is presented. The representations are derived in a purely algebraic way. The generators are represented in terms of tensor products of matrices 2n by 2n and polynomial functions of nine noncommuting variables psub(j), qsub(j), qsub(j)sup(-1), j=1, 2, 3, the psub(j), qsub(j) satisfying the canonical commutation relations. Besides the discrete parameter n, the representations are labelled by a continuous real parameter - the eigenvalue of the second-order Casimir operator. The even generators are represented skew-symmetrically and this property is shown to imply that each of the representations in the family is equivalent to a representation of the para-Bose algebra pB(2) having the physical ''star properties'': the creation and annihilation operators are adjoint to each other. (Atomindex citation 14:773121)