Quasi-Unitary Three-Particle Approximations

The three-particle discontinuity equations are expressed in forms convenient for the study of unitarity violations. As an application, the constraints on the two-particle transition operators imposed by requiring consistency with three-particle unitarity are deduced. This provides a framework for some recent proposals for generating approximate, finite-rank, two-particle transition operators which do not satisfy off-shell unitarity. Also, the general features of some quasi-unitary impulse approximations are discussed in a unified fashion in order to clarify the conditions for their validity as well as for higher-order quasi-unitary approximations.