| Certain well-known difficulties are encountered in current theories describing elementary particles by quantized wave fields. Notably, divergent integrals result from computations of physically-observable quantities which are known to be finite. As a consequence, a number of techniques have been suggested recently for removing these infinities.; An analysis is made of one such proposal, that of a non-local interaction between the fields. It is assumed that the interaction energy density is a function of field operators at three points, instead of just one, a form function being used to weight more heavily contributions from nearby points. The additional freedom provided by the introduction of the somewhat-arbitrary form function is sufficient to permit making previously-divergent integrals converge.; It is shown that, for the most general form function, an energy-momentum tensor and a charge-current four-vector in the usual sense will not satisfy a differential continuity equation; energy, momentum, charge, and current are conserved only over the collision as a whole. As a result, a Hamiltonian in the familiar form does not exist, and it is necessary to find the S-matrix for the process directly from the equations of motion. A method of doing this is presented. Rules analogous to those Feynman and Dyson are developed, so that the matrix element for a given process may be written down directly.; The theory is made relativistically-covariant, invariant under charge conjunction, and invariant under changes in gauge of an external electromagnetic field, by placing various restrictions upon the form function. These restrictions limit the form function to be a function of only three variables. It is shown that the non-local interaction gives results similar to those which would be obtained from a theory providing for the propagation of virtual particles from one point of the interaction to the other, with the form function merely giving the distribution in masses of these virtual particles. (Abstract shortened by UMI.)... |
