Functional Quantum Theory of Scattering

Dynamics of quantum field theory can be formulated by functional equations. To develop a complete functional quantum theory the physical information has to be given by functional operations only. The most important physical information of elementary particle physics is the Ä-matrix. In this paper the functional ^-matrix is constructed for the scattering of relativistic dressed particles, i.e. for particles with structural properties. The basic functional equation is assumed to be derived from a nonlinear spinor field equation with noncanonical relativistic Heisenberg quantization. The initial free dressed many particle states are defined, and the scattering functionals are constructed. By the use of irre ducible representations the equivalence of the functional ^-matrix with the conventional Hilbert space definition is shown with respect to an appropriate definition of the functional scalar product. Technical details are discussed in the appendices.