Gravitational-scalar field coupling II: James H. Higbie. Department of Physics, Brandeis University, Waltham, Massachusetts and Technion-Israel Institute of Technology, Haifa, Israel

Abstract

This chapter discusses the dynamical equations and approximation method. The integral equations approach to the three-body problem, decisively stimulated by Faddeev's formulation, provides the most powerful tool for studying the internal structure of this system. An essential step toward a detailed understanding of composite particle dynamics has been done in this way. The search for adequate extensions to the general N-body situation represents a natural challenge. Emphasizing different aspects of the three-body theory, different generalizations have been found. It was the concept of connectedness of the integral kernel that represented the guiding idea of almost all proposals. The four-body problem shows already the typical difficulties of the general case. In the Faddeev case, it can be shown that after a sufficient number of iterations, the kernel becomes even completely continuous. The advantage of such a procedure is that the completeness does not have to be assumed but is directly proved.