ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The method presented in the first part of this work is applied to the superalgebra B(0,2). Two families of irreducible *-representations of this superalgebra and its real form osp(1,4) are constructed explicitly in terms of differential operators on the Hilbert space L2(M˜)⊗CN of N-component vector functions Ψ: M˜→CN@B: (i) the family {πJ@B: J=0,1,...} of massless representations with N=2, M˜=R+×(−π,π)×R+, the dimension of the vacuum subspace of πJ being J+1; (ii) the family {π(cursive-theta)0@B: cursive-theta〉0} of massive representations such that π(cursive-theta)0(up harp-r)so(3,2) equals the direct sum of three irreducible representations of so(3,2). This family is characterized by N=4, M˜=R+×(0,π)×R+ and nondegenerated vacuum. It is also shown that all the remaining massive representations form a system of families {π(cursive-theta)J@B: cursive-theta〉J/2}, J=1,2,..., with N=4(J+1), (J+1)-fold degenerated vacuum and common M˜=R+×(0,π)×R+.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.528048
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