Relativity and spin in one-, two-, and three-body systems

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Abstract
The method used to define relativistic one-, two-, and three-particle states with spin in the z basis and the helicity basis is described, and the Lorentz transformation and improper transformation properties of these states are discussed. The three-body states are used to construct a relativistic, three-body, angular-momentum recoupling coefficient. A detailed derivation of this recoupling coefficient in both the z basis (LS coupling scheme) and the helicity basis is presented, and an expression for the nonrelativistic limit of this recoupling coefficient (i.e., neglecting Wigner spin precession) is given. Uses of these states in relativistic potential theory and optical model problems is also discussed.