Spin-mass content of the Bhabha particle and the group chain SU(4)supersetof Sp(4)superset of SU(2)xU(1)

The relativistic particles described by the Bhabha equation (Bhabha particl es) can possess several values of masses (M-tau = n/2 tau) and spins s less than or equal to n/2. In order to find the spin-mass content of such parti cles corresponding to the general irrep [n(1)n(2)] of the group Sp(4)simila r to O(5) which is the symmetry group of the Bhabha equation, the noncanoni cal chain of groups Sp(4)superset of SUs(2) x U-tau(1) is considered. In th is paper, we construct the basis of the irrep [n(1)n(2)] in a boson realiza tion form using the method of elementary permissible diagrams. This is achi eved by the introduction of special "symplectic" bosons. The maximum and mi nimum values of spin s are established for each value of tau. The multiplic ity of degenerate pairs (s,t) can be easily calculated with the help of the generating function obtained in this paper. (C) 1999 American Institute of Physics. [S0022-2488(99)01908-8].