Yang-Mills-Utiyama Theory and Graviweak Correspondence

TL;DR

This paper develops a geometrical Yang-Mills framework incorporating gravity, extending it to broader spaces, and proposes a novel connection between gravity and the weak force called the graviweak correspondence.

Contribution

It introduces an extended Yang-Mills theory that unifies gravity and internal gauge symmetries, establishing a new relation between gravity and the weak interaction.

Findings

Extended Yang-Mills theory in broader spaces.

Transport of topological features from Euclidean to Lorentzian spaces.

Proposal of the graviweak correspondence linking gravity and weak force.

Abstract

This report provides a geometrical Yang-Mills theory, including gravity. The theory treats the space-time symmetry of the local Lorentz group in the same manner as the internal gauge symmetry. We extend this general relativistic Yang-Mills theory in the Minkowski space-time to a broader space, including Euclidean and Minkowskian spaces. In the extended space, we can transport topological achievements from the Euclidean Yang-Mills theory into the Lorentzian Yang-Mills theory. This extension also provides a relation between space-time and internal symmetry. The perspective provided by the extended theory suggests the novel relation between gravity and the weak force, leading us to the graviweak correspondence.