Field Theory of Elementary Domains and Particles.II

概要

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Formulation and its consequences of the theory outlined in the preceding paper are presented and analyzed. The field is defined on the closed domain in the spacetime world and is described by fourteen variables, i.e. by the coordinates of the center, invariant deformable lengths and generalized four-dimensional Euler angles. The combination of six Euler angles and two invariant lengths gives a complex four-component spinor operator by which the eigenstates of internal spin are determined. The fundamental field equation is introduced based on a simple geometric consideration of periodicity among the elementary domains and analyzed on a line similar to the infinite component theory. Also the second quantization is discussed mainly in connection with the finite difference character of the field equation and the simultaneous preparation of the four-dimensional manifold is assured from the commutability of the fields of domains separated by a finite distance in space-like and time-like directions. A possibility of introducing the internal symmetry such as SU(6) is also suggested in connection with possible choice of the four invariant lengths to be amalgamated in constructing the spinor operators. The interaction scheme in this theory is only sketched and left to future investigations.
理論物理学刊行会の論文
1968-10-25