An Attempt to the Unified Description of Elementary Particles

Publisher Website
Google Scholar
Abstract
An attempt is made to give a unified and a more positive definition of elementary particles by introducing a substance of higher level than them. This substance is named “Urmaterie”, and is assumed to be described by a non-local field proposed by Yukawa. Various states of the internal motion of Urmaterie are classified by eigenvalues of a complete set of mutually commutative operators with respect to internal coordinates, two of which can be taken as the spin and the mass operators. Each eigenstate thus classified is assumed to correspond to the elementary particle of the present theory. In §1, the present situation of the theory of elementary particles is analysed, and the phenomenological feature of the present theory and the necessity of introducing a substance of higher level to overcome it is stressed. In §2, the spin and the mass operators are introduced. It is done according to the principle that the structure of elementary particles should determine uniquely the transformation properties of the wave functions under Lorentz-transformations. The equations of motion of Urmaterie are then derived from korrespondenzmässig considerations and from the principle of reciprocity. In §3, the eigenvalue and the eigenfunction of the mass operator is given in the simplest case when the Urmaterie field is assumed as scalar. In §4, the relation of this Urmaterie field to the local field is discussed, and it is shown that, in the case of the scalar as before, the equation of motion of Urmaterie reduces to that of Fierz for eigenstates of the spin and the mass operators. In §5, a qualitative discussion on the interaction of Urmaterie is given. In §6, an extension to the case of spinor is discussed. It is shown that the existence of a new structure constant other than the spin and the rest mass inevitably follows. It is shown that this is interpretable as expressing the essential difference of the heavy and light particles, and in its connection an attempt is made to deduce the conservation law of heavy particles. In §7, the deductive perspective and the further outlook of the theory is briefly given.

This publication has 0 references indexed in Scilit: