Application of Lie algebroid structures to unification of Einstein and yang-mills field equations

TL;DR

This paper explores the use of Lie algebroid structures to unify Einstein and Yang-Mills field equations within a single framework, potentially leading to new testable predictions.

Contribution

It introduces a novel approach by formulating Einstein and Yang-Mills equations in an algebroid bundle, unifying gravitational and gauge fields.

Findings

Unified Einstein-Yang-Mills equation derived in algebroid framework

Potential for new experimental predictions from the unified equation

Demonstrates feasibility of describing gravity and gauge forces together

Abstract

Yang-mills field equations describe new forces in the context of Lie groups and principle bundles. It is of interest to know if the new forces and gravitation can be described in the context of algebroids. This work was intended as an attempt to answer last question. The basic idea is to construct Einstein field equation in an algebroid bundle associated to space-time manifold. This equation contains Einstein and yang-mills field equations simultaneously. Also this equation yields a new equation that can have interesting experimental results.