The non-Abelian Weyl-Yang-Kaluza-Klein gravity model

TL;DR

This paper develops a higher-dimensional non-Abelian Kaluza-Klein gravity model based on Weyl-Yang theory, deriving new field equations and stress-energy tensors that unify gravity and gauge interactions with novel source terms.

Contribution

It introduces a generalized non-Abelian Weyl-Yang-Kaluza-Klein model with explicit internal space reduction and new gravitational source terms not previously documented.

Findings

Derived dimensionally reduced field equations and stress-energy tensors.

Established interactions between gravitational and gauge fields in a non-Abelian framework.

Identified new gravitational source terms and Yang-Mills force densities.

Abstract

The Weyl$-$Yang gravitational gauge theory is investigated in the structure of a pure higher-dimensional non-Abelian Kaluza$-$Klein background. We construct the dimensionally reduced field equations and stress-energy-momentum tensors as well as the four dimensional modified Weyl$-$Yang$+$Yang$-$Mills theory from an arbitrary curved $internal$ space in the anholonomic frame which are the extensions of our previous model for the non-Abelian case. In particular, the coset space reduction is considered to explicitly obtain the interactions between the gravitational and the gauge fields. The resulting equations not only appear to be generalization of the well-established equations of non-Abelian theory but also contain intrinsically the generalized gravitational source term which does not exist in the literature so far and the Yang$-$Mills force density which is exactly equivalent to the negative gradient of a Yang$-$Mills quadratic invariant.