# Coupling the Dirac and Einstein equations through geometry

## TL;DR

This paper presents a geometric framework using the exterior algebra bundle over curved spacetime to derive and couple the Dirac and Einstein equations from a variational principle, suggesting a unified approach to fundamental physics.

## Contribution

It introduces a novel geometric approach that derives both Dirac and Einstein equations and their coupling from a single variational principle within the exterior algebra bundle.

## Key findings

- Derivation of Dirac and Einstein equations from geometric invariants
- Coupling of these equations within a unified variational framework
- Potential for incorporating other forces geometrically

## Abstract

We show that the exterior algebra bundle over a curved spacetime can be used as framework in which both the Dirac and the Einstein equations can be obtained. These equations and their coupling follow from the variational principle applied to a Lagrangian constructed from natural geometric invariants. We also briefly indicate how other forces can potentially be incorporated within this geometric framework.