New integral equations in the theory of four-particle scattering

The four-particle problem is studied through the resolvent operator G of its Hamiltonian. The quantity G is decomposed into a product of five factors. Four of them may be found from the solutions of three-particle problems, or the solutions of four-particle problems with less than six pair potentials. The fifth factor is shown to be a unique solution of an integral equation with a connected kernel. Along the same line a formal solution is presented for the components of the four-particle T-operator. The resulting system of integral equations is free of two-body potentials and contains only scattering operators. Finally an equation for the bound-state wave function is given, and its equivalence with the Schrödinger equation is explicitly demonstrated.