Relativistic Three-Particle Equations. I

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Abstract
Linear integral equations for three-particle scattering amplitudes in any Lorentz-invariant local field theory are written; they are three-particle analogs of the Bethe-Salpeter equation. The kernels of these equations are off-mass-shell relativistic generalizations of two-particle and three-particle potentials. We transform the equations by the method of Faddeev so that the two-particle potential no longer appears, but only the two-particle scattering amplitude. Particular cases of these equations are presented. We then show that two- and three-particle unitarity is satisfied provided the relativistic potentials are real in the relevant energy region.