Relativistic few-body problem. II. Three-body equations and three-body forces

Publisher Website
Google Scholar
Abstract
Examination of the sum of all ladder and crossed ladder exchanges between three particles leads to a set of relativistic three-body equations of the Faddeev type in which two of the three particles are restricted to their mass shell. The choice of which two particles are on shell at a given instant is uniquely determined by the requirement that they be spectators either before or after the interaction. It is shown that these equations satisfy the cluster property, and the two-body amplitudes which drive the equations are known in principle. Three-body unitarity is proved. Three-body forces which arise from the underlying dynamics are discussed, classified, and estimated numerically for a spinless example. It is found that the three-body forces tend to cancel to some extent, are sensitive to the details of the dynamics, and that contributions to such forces, primarily of relativistic origin, can be important.