Formulation of Field Theories of Composite Particles

Abstract

Based upon Feynman's over-all-space-time point of view, a general method for dealing with bound-state problems is presented. In this paper we are mainly interested in the properties of Green's functions that should be satisfied in the field theories with bound states. First the Chew-Low or Lehmann-Symanzik-Zimmermann equations are generalized so as to include composite particles. Then we examine the possibility of distinguishing between elementary and composite particles. Finally, an investigation is made of how the $S$ matrix elements for processes involving composite particles are related to those involving no composite particles. This problem is illustrated by the relation between $p+p\to n+p+{\pi }^{+}$ and $p+p\to d+{\pi }^{+}$.