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

摘要

Pandres has developed a theory in which the geometrical structure of a realfour-dimensional space-time is expressed by a real orthonormal tetrad, and thegroup of diffeomorphisms is replaced by a larger group called the conservationgroup. This paper extends the geometrical foundation for Pandres' theory bydeveloping an appropriate covariant derivative which is covariant under alllocal Lorentz (frame) transformations, including complex Lorentztransformations, as well as conservative transformations. After defining thisextended covariant derivative, an appropriate Lagrangian and its resultingfield equations are derived. As in Pandres' theory, these field equationsresult in a stress-energy tensor that has terms which may automaticallyrepresent the electroweak field. Finally, the theory is extended to include2-spinors and 4-spinors.