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

TL;DR

This paper extends Pandres' unified field theory by developing a covariant derivative invariant under all local Lorentz and conservative transformations, deriving corresponding field equations, and incorporating spinor fields.

Contribution

It introduces a covariant derivative covariant under all local transformations, extends the geometric framework, and incorporates spinor fields into Pandres' unified theory.

Findings

Derived a new covariant derivative for conservative transformations.

Obtained field equations with a stress-energy tensor including electroweak terms.

Extended the theory to include 2-spinors and 4-spinors.

Abstract

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.