A New Viewpoint on the Space-Time Model of Elementary Particles. I

概要

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In two papers (of which this is the first) an attempt has been made to describe the pseudo-unitary group U(3,1) of particle physics on the basis of a classical formulation of the nonlocal theory of Yukawa in contrast to quantum mechanical approach of Takabayasi, Shin and others. This is done by describing the group U(3,1) as the structural group of the frame bundle of the eight-dimensional classical relativistic space B_<6,2>= (X,y) (where X denotes the external co-ordinates and y the internal co-ordinates of Yukawa). Such a classi-cal approach to the group U(3,1) has the novel feature of enabling us to interpret the gauge vector fields and the gauge tensor fields, which are associated with the gauge ex-tension of this group, as the manifestation of the local connexion and the local curvature of the classical space B_<6,2>. This is achieved by postulating that the classical gauge fields give rise to a strong inhomogeneity in the neighbourhood of a point of the B_<6,2> space so that there exists a y-dependent Riemann curvature in this space. Then by interpreting the group U(3,1) as the group of holonomy of B_<6,2> it is shown that the expansion coefficients of the connexion and curvature of the tangent bundle of B_<6,2>, which are elements of the holonomy group of _<6,2>, constitute the bilocal generalisation of the gauge vector field and the gauge tensor field of Yang and Mills, respectively.
理論物理学刊行会の論文
1971-01-25