Diffeomorphism Invariance and Local Lorentz Invariance

TL;DR

This paper explores how diffeomorphism and local Lorentz invariance in Maxwell and Dirac-Hestenes equations lead to equivalences among different universe models with varying geometric properties.

Contribution

It demonstrates that invariance principles imply equivalence among universe models with different connections, torsion, and curvature, revealing deep geometric symmetries.

Findings

Diffeomorphism invariance implies equivalence among universe models with different torsion and curvature.

Local Lorentz invariance leads to equivalence among models with different G-connections.

Different universe models can be equivalent under invariance principles despite geometric differences.

Abstract

We show that diffeomorphism invariance of the Maxwell and the Dirac-Hestenes equations implies the equivalence among different universe models such that if one has a linear connection with non-null torsion and/or curvature the others have also. On the other hand local Lorentz invariance implies the surprising equivalence among different universe models that have in general different G-connections with different curvature and torsion tensors.