Nuclear, Algebraic Surfaces and SO(10)

Abstract

In this paper nuclear representations of the Dirac ring, developed over many years, are shown to be a particular case of a theorem in algebraic geometry which at the same time associates them with a Hodge decomposition of a Kaehler manifold. This yields a shape illustrated by Figs. 1,2,3 which in some cases is independent of any appeal to a symmetry group. However because the odd-A nuclear representations are in the infinitesimal ring of SO(4) and the internal space of each representation is in a Kaehler (even Calabi Yau) manifold K; the group SO(10) = SO(4) × K can give additional information. This paper develops the very fruitful symbiosis between algebra and irreducible representations of SO(10) and shows that the odd-A nucleus is bound by a self-generating string field, whose quanta are the mesons, which therefore dispenses with nuclear forces and reduces nuclear structure to geometry. An appendix gives and example of how the theory may be applied to laser cooling.