Riemannian gauge theory and charge quantization

In a traditional gauge theory, the matter fields \phi^a and the gauge fieldsA^c_\mu are fundamental objects of the theory. The traditional gauge field issimilar to the connection coefficient in the Riemannian geometry covariantderivative, and the field-strength tensor is similar to the curvature tensor.In contrast, the connection in Riemannian geometry is derived from the metricor an embedding space. Guided by the physical principal of increasing symmetryamong the four forces, we propose a different construction. Instead of definingthe transformation properties of a fundamental gauge field, we derive the gaugetheory from an embedding of a gauge fiber F=R^n or F=C^n into a trivial,embedding vector bundle F=R^N or F=C^N where N>n. Our new action is symmetricbetween the gauge theory and the Riemannian geometry. By expressinggauge-covariant fields in terms of the orthonormal gauge basis vectors, werecover a traditional, SO(n) or U(n) gauge theory. In contrast, the new theoryhas all matter fields on a particular fiber couple with the same couplingconstant. Even the matter fields on a C^1 fiber, which have a U(1) symmetrygroup, couple with the same charge of +/- q. The physical origin of this uniquecoupling constant is a generalization of the general relativity equivalenceprinciple. Because our action is independent of the choice of basis, itsnatural invariance group is GL(n,R) or GL(n,C). Last, the new action alsorequires a small correction to the general-relativity action proportional tothe square of the curvature tensor.Comment: Improved the explanations, added references, added 3 figures and an appendix, corrected a sign error in the old figure 4 (now figure 5). Now 33 pages, 7 figures and 2 tables. E-mail Serna for annimation