A formal derivation of the general unitarity relation for the four-particle transition operator is obtaihed by generalizing the method of matrix algebra for the three-body amplitude developed by Alt, Grassberger and Sandhars to the four-body case. From the operator relation obtained, the on-shell unitarity relation for the amplitudes that describe elastic/rearrangement, partial breakup, and full breakup scattering processes are derived by taking the matrix elements of the operator between appropriate initial and final states.
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