Relativistic three-body problem in relative variables

A Lorentz covariant three-body theory is constructed in the momentum representation in the framework of the three-dimensional formulation of quantum field theory. Relativistic Jacobian momenta are introduced by means of the operation of composition of four-vectors in Lobachevskii space. It is shown that the cms motion can be separated out and the problem is formulated solely in relative variables as a direct generalization of the nonrelativistic theory. Three-dimensional relativistic analogs are obtained of the Faddeev equations for the scattering amplitude and also an analog of the Schrödinger equation in relative variables for a three-body system. The formulation satisfies three-particle unitarity and the correspondence principle.