Field Theory of Elementary Domains and Particles. I

Abstract

In §1 and §2, a brief historical account was given on the developments in our efforts to construct a unified theory of elementary particles based on the assumption that each particle is a quantum mechanical object extended in space and time. As the most simple model, essential features of field theory are discussed first. Generalization to multilocal field and the derivation of various quantum numbers, which are ascribed to hadrons, from the quantization of internal motion are described. To the models based on multilocal field theory, geometrical constraint is imposed, for the purpose of obtaining half integer spin states as well as spin states. Similarity of such a case to the continuous deformable body subject to quantization is pointed out. The concept of elementary domain is introduced as a natural consequence of treatment of system of many extended particles according to the method of second quantization in nonrelativistic theory. In §3, §4 and §5, relativistic theory of elementary domains is developed. Elementary particles are interpreted as sequences in time of the excited states of the four-dimensional elementary domain which is regareded as quantum mechanical object. As the substitute for Schrodinger wave equation in quantum mechanics of point particles, a new type of wave equation, which connect elementary domains separated by a finite amount from each other in space and time, is proposed. It is essentially a difference equation with respect to the displacement of the center of the domain. Multiplicity of the solutions of this difference-type equation gives rise to a new feature which seems to open a way unknown toward the solution of the problem of convergence. Detailed account is left to Part II of this paper.