Unified Field Theory From Enlarged Transformation Group. The Consistent Hamiltonian

TL;DR

This paper develops a Hamiltonian formulation of a unified field theory based on an enlarged transformation group, which extends general relativity to include electroweak fields and discusses future extensions to strong interactions.

Contribution

It introduces a consistent Hamiltonian for a unified field theory with an enlarged symmetry group, bridging geometry and gauge fields.

Findings

The Hamiltonian formulation is consistent with Einstein's equations.

The theory incorporates electroweak fields naturally.

Discussion on extending the framework to include strong interactions.

Abstract

A theory has been presented previously in which the geometrical structure of a real four-dimensional space time manifold is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group. The group enlargement was accomplished by including those transformations to anholonomic coordinates under which conservation laws are covariant statements. Field equations have been obtained from a variational principle which is invariant under the larger group. These field equations imply the validity of the Einstein equations of general relativity with a stress-energy tensor that is just what one expects for the electroweak field and associated currents. In this paper, as a first step toward quantization, a consistent Hamiltonian for the theory is obtained. Some concluding remarks are given concerning the need for further development of the theory. These remarks include discussion of a possible method for extending the theory to include the strong interaction.