A New Viewpoint on the Space-Time Model of Elementary Particles. II : Space-Time Description of Gauge Fields

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We continue the development started in the preceding paper in which we described the non-compact group U(3・1) as the structural group of the tangent-bundle of an eight-dimensional Kahlerian manifold B_<6,2> built from the four space-time co-ordinates X^r, the four internal psace-time co-ordinates y^r of Yukawa, and a y-dependent Riemannian metric. In this paper we shall consider the above group as the group of holonomy of B_<6,2> and as a consequence of this point of view we shall arrive at an interpretation of the group as the generalised gauge group, without having to rely on the use of the action principle. In such an interpretation the gauge fields will be implicit in the geometry; they will, in particular, be a manifestation of the Christoffel connection of the B_<6,2> space in complete analogy with the Christoffel connection of general relativity.
理論物理学刊行会の論文
1971-02-25