N -Body Relativistic Scattering Theory

A set of coupled linear integral equations is proposed as a means of generating Lorentz-invariant multiparticle scattering amplitudes which satisfy truncated unitarity relations. Steady-state nonrelativistic scattering theory, in particular the version based on the generalized Faddeev equations, is used as a guide in the formulation and physical interpretation of the equations. The input to the integral equations is a set of scattering amplitudes for subsystems of particles. Creation and annihilation processes are described by the interchange of terminal-state scattering amplitudes with vertex functions, in complete formal analogy with the nonrelativistic treatment of break-up and capture events. A wave function is introduced, a conserved current is defined, and a perturbation theory for discrete states is set up. Formulas for transition rates, for reaction and decay processes, are derived which agree with the familiar results of time-dependent Hamiltonian theory. The possibility that self-consistency criteria might provide a basis for the determination of the input amplitudes is noted.