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) [SU(2) SU(2)). In the present paper we find that the symmetry group of the problem rather than SU(4) is its smaller subgroup Sp(4) which 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 generators of O(5) O(4) O(3) O(2) groups. These are more convenient as there are no multiplicity indices and the matrix elements on the generators can be given explicitly for an arbitrary irrep (n1n2) of O(5). The analysis is applied variationally to particles in an harmonic oscillator potential corresponding to the irreps (1/2 1/2), (11), (10),(3/2 3/2) of O(5). (Author)