Gravitational and electroweak unification by replacing diffeomorphisms with larger group

The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers will agree whether any given quantity is conserved. Alternatively, and equivalently, it is defined by the assumption that all observers will agree that the general relativistic wave equation describes the propagation of light. Thus, the group replacement is analogous to the replacement of the Lorentz group by the diffeomorphisms that led Einstein from special relativity to general relativity, and is also consistent with the assumption of constant light velocity that led him to special relativity. The enlarged covariance group leads to a non-commutative geometry based not on a manifold, but on a nonlocal space in which paths, rather than points, are the most primitive invariant entities. This yields a theory which unifies the gravitational and electroweak interactions. The theory contains no adjustable parameters, such as those that are chosen arbitrarily in the standard model.Comment: 28 pages

Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations

Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group. This paper extends the geometrical foundation for Pandres' theory by developing an appropriate covariant derivative which is covariant under all local Lorentz (frame) transformations, including complex Lorentz transformations, as well as conservative transformations. After defining this extended covariant derivative, an appropriate Lagrangian and its resulting field equations are derived. As in Pandres' theory, these field equations result in a stress-energy tensor that has terms which may automatically represent the electroweak field. Finally, the theory is extended to include 2-spinors and 4-spinors.Comment: Aug 25 replacement has corrected margin width