A SOLVABLE RELATIVISTIC 4-BODY COMPOSITE SYSTEM IN 1+1 DIMENSIONS AND NEW INTRINSIC COUPLINGS BETWEEN ITS STRUCTURE AND OVERALL TRANSLATIONAL MOTION

We study a system of few Dirac particles interacting via pairwise delta function potentials and forming a bound state in two dimensional space-time, in connection with previous works of the three-and two-body cases. The relativistic covariance of the model is guaranteed by the existence of the Lorentz boost operator. Rediscussing results in the three- and two-body cases, we provide a set of Ansatze to find exact solutions of the N greater-than-or-equal-to 4-body cases and present the exact solution of the N = 4 case explicitly. The resultant four-body bound-state solution contains two new dynamical factors representing new effects due to the coupling of the structure of the bound state with the overall translational motion of the bound state, in comparison with the solution of the two-body case. One of the new dynamical factors is seen in the solution of the three-body case and vanishes in the rest frame of the bound state, while the other is quite new and survives in the rest frame. It is strongly conjectured that with increasing N, new modes appear more and more about the coupling of the structure of the bound state with the overall translational motion of the bound state.