  In a traditional gauge theory, the matter fields \phi^a and the gauge fields
A^c_\mu are fundamental objects of the theory. The traditional gauge field is
similar to the connection coefficient in the Riemannian geometry covariant
derivative, and the field-strength tensor is similar to the curvature tensor.
In contrast, the connection in Riemannian geometry is derived from the metric
or an embedding space. Guided by the physical principal of increasing symmetry
among the four forces, we propose a different construction. Instead of defining
the transformation properties of a fundamental gauge field, we derive the gauge
theory 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 symmetric
between the gauge theory and the Riemannian geometry. By expressing
gauge-covariant fields in terms of the orthonormal gauge basis vectors, we
recover a traditional, SO(n) or U(n) gauge theory. In contrast, the new theory
has all matter fields on a particular fiber couple with the same coupling
constant. Even the matter fields on a C^1 fiber, which have a U(1) symmetry
group, couple with the same charge of +/- q. The physical origin of this unique
coupling constant is a generalization of the general relativity equivalence
principle. Because our action is independent of the choice of basis, its
natural invariance group is GL(n,R) or GL(n,C). Last, the new action also
requires a small correction to the general-relativity action proportional to
the square of the curvature tensor.
