Observable processes corresponding to a fundamental field

Abstract

One herein constructs the amplitude for elastic scattering corresponding to a neutral, fundamental field. The fundamental field ϕ(x) can be written as a generalized free field which transforms locally under the Poincare group, and has a propagator which by analytic continuation can be shown to carry an infinite tower of spinning self-compounds lying on a Regge trajectory. The propagator of the neutral field is invariant underTP. To construct the amplitude, one first sets up all phenomenological asymptotic states of one, two, three, etc. particles corresponding to the discrete, stable mass component of the fundamental field. These states, used as a complete set of intermediate states, enable one in principle through unitarity of Δαβ+(x-y)= to calculate the vertex function of these phenomenological states with respect to the fundamental field. These vertex functions can then be used to determine the corresponding scattering amplitude: for example, the elastic-scattering amplitude of two mass-m0, spin-0 particles. For the latter one uses unitarity again and in fact in the states of the fundamental free field. The present paper is a preliminary investigation of the determination of these observable scattering amplitudes corresponding to a fundamental field. The elastic-scattering amplitude can be continued in the angular momentum under the same conditions as the propagator of the fundamental field, and the spin trajectory is completely determined by the spectral function of this propagator.