Field-Theory Realization of the Droplet Model

We demonstrate with two field-theoretic models that the operator droplet model proposed by Chou and Yang can be understood as due to the contribution from a class of leading Feynman diagrams at $s=\ensuremath{\infty}$. In the first model, we consider a theory which consists of both a strong and an electromagnetic interaction. The purpose of introducing two types of interactions is to supply a natural division between the production of particles and the interaction between the jets. In this model, the sum of pure photon-exchange diagrams leads automatically to an expression identical to that of the operator droplet model. Limitations and generalizations of the model are investigated. The second model is derived from pure quantum electrodynamics. We find that an operator-droplet-model formulation can reproduce leading amplitudes in quantum electrodynamics, including those which give rise to ${(\mathrm{ln}s)}^{N}$ behavior. This confirms and generalizes an earlier result of Lee. We demonstrate explicitly how the $N$-bubble diagrams should be treated in this calculation. By including diagrams related to one another by covariance, a reference-frame-independent result always emerges. These frame-independent results coincide with earlier calculations based on the usual Feynman rules.