Classical unified field theories describe the properties of the electromagnetic field as a purely geometric phenomenon. Einstein tried to form a generalized theory of gravitation that would unify the gravitational and electromagnetic forces (and perhaps others), guided by a belief in a single origin for the entire set of physical laws. These attempts initially concentrated on additional geometric notions such as vierbeins and "distant parallelism", but eventually centered around treating both the metric tensor and the affine connection as fundamental fields. (Because they are not independent, the metric-affine theory was somewhat complicated.) In general relativity, these fields are symmetric (in the matrix sense), but
Classical unified field theories noted that in addition to a metric field there could be additional degrees of freedom along a path between two points in a manifold, and he tried to exploit this by introducing a basic method for comparison of local size measures along such a path, in terms of a gauge field. This geometry generalized Riemannian geometry in that there was a vector field "Q", in addition to the metric "g", which together gave rise to both the electromagnetic and gravitational fields. This theory was mathematically sound, albeit complicated, resulting in difficult and high-order field equations. The critical mathematical ingredients in