Structure and Mass Spectrum of Elementary Particles. I. General Considerations

Abstract

As discussed in previous papers,1 the nonlocal field was introduced in order to describe relativistically a system which was elementary in the sense that it could no longer be decomposed into more elementary constituents, but was so substantial, nevertheless, as to be able to contain implicitly a great variety of particles with different masses, spins, and other intrinsic properties. However, the conclusions reached so far were very unsatisfactory in many respects.2 Among other things, the masses of the particles associated with the irreducible nonlocal fields remained completely arbitrary and simple and plausible assumptions concerning the interaction between fields did not result in the expected convergence of self-energies. It seems to the author that these disappointing consequences are not inherent in nonlocal field theory, in general, but are rather related to the particular type of field to which the author restricted himself. Instead, if we start anew from less restricted nonlocal fields, a more promising aspect of possible nonlocal theories is revealed, as shown in the following.