Basis states for relativistic three-body calculations of particles with spin

Using a linear combination of the three-body helicity states constructed by Wick, a new set of basis states is constructed that can be used to perform three-body calculations with relativistic treatment of the spin. These states are diagonal in the usual angular momentum quantum numbers of a pair l _iS_ij_i, where l_i is the orbital angular momentum, S_i the spin, and j_i the total angular momentum of the pair jk. These states are used to write down the relativistic Faddeev equations obtaining two sets of uncoupled integral equations that are identified as corresponding to the states of positive and negative parity. It is also shown, by means of some simple examples, that the relativistic recoupling coefficients reduce to the usual nonrelativistic ones if one neglects the effects of relativity. Some possible applications involving particles off the mass shell are discussed.