ANALYSIS OF RELATIVISTIC-PARTICLES OF ARBITRARY SPIN THROUGH DIFFERENT CHAINS OF GROUPS

In a previous paper we analyzed the equation of particles of arbitrary spins characterized by the chain of groups SU(4) superset of [S (U) o ver cap(2) x SU(2)]. In the present paper we find that the symmetry gr oup of the problem rather than SU(4) is its smaller subgroup Sp(4) whi ch is a unitary symplectic one. As Sp(4) is isomorphic to O(5) we can replace it by the latter and write our equation in terms of the genera tors of O(5) superset of O(4) superset of O(3) superset of O(2) groups . These are more convenient as there are no multiplicity indices and t he matrix elements of the generators can be given explicitly for an ar bitrary irrep (n(1)n(2)) of O(5). The analysis is applied variationall y to particles in an harmonic oscillator potential corresponding to th e irreps (1/2 1/2 ), (11), (10), (3/2 3/2) of O(5).