Operator Formulation of the Droplet Model

Abstract

We study in detail the implications of the operator formulation of the droplet model. The picture of high-energy scattering that emerges from this model attributes the interaction between two colliding particles at high energies to an instantaneous, multiple exchange between two extended charge distributions. Thus the study of charge correlation functions becomes the most important problem in the droplet model. We find that in order for the elastic cross section to have a finite limit at infinite energy, the charge must be a conserved one. In quantum electrodynamics the charge in question is the electric charge. In hadronic physics, we conjecture, it is the baryonic charge. Various arguments for and implications of this hypothesis are presented. We study formal properties of the charge correlation functions that follow from microcausality, $T$, $C$, $P$ invariances, and charge conservation. Perturbation expansion of the correlation functions is studied, and their cluster properties are deduced. A cluster expansion of the high-energy $T$ matrix is developed, and the exponentiation of the interaction potential in this scheme is noted. The operator droplet model is put to the test of reproducing the high-energy limit of elastic scattering in quantum electrodynamics found by Cheng and Wu in perturbation theory. We find that the droplet model reproduces exactly the results of Cheng and Wu as to the impact factor. Infact, the "impact picture" of Cheng and Wu is completely equivalent to the droplet model in the operator version. An appraisal is made of the possible limitation of the model.