Space-Time Model of Elementary Particles and Unitary Symmetry. I: General Foundation and Symmetry

Abstract

The general framework is given of a unified theory of elementary particles based on the hypothesis that a particle should be association of four space-time points. With the separation of the center-or-mass degree of freedom the relative motion of the system is described by a set of three normal axes. The equivalence of the normal axes implies the O(3) symmetry which is independent of the Lorentz transformation. The wave equation contains an invariant potential representing a strong direct non-local interaction working inside the particle to ensure that the motion of normal coordinates is of oscillator-type maintaining the four-point association within a small space-time region (with a characteristic length). This entails the wider U(3) symmetry that includes the above O(3) subgroup as well as the internal self-reciprocity. In this model the unitary spins including isospin and hypercharge originate from excitations of oscillatory motions of normal axes with respect to the figure space, while the spin is due to the rotational part of the relative motion with respect to the inertial frame. If in the system one of the four points becomes inequivalent with the other three, it implies the usual symmetry-breaking of U(3). The meaning of the required triality condition is considered. The whole treatment is made in conformity with relativistic covariance, but on the level of one-particle theory.