Spinor fields without Lorentz frames in curved spacetime using complexified quaternions

TL;DR

This paper introduces a novel formalism using complexified quaternions to handle tensor and spinor fields in curved spacetime without relying on Lorentz frames or vierbeins, potentially linking to electromagnetism.

Contribution

It presents a Lorentz-frame-free formalism for spinor and tensor fields in curved spacetime using complexified quaternions, with a natural emergence of a U(1) gauge symmetry.

Findings

Formalism avoids Lorentz frames and vierbeins

U(1) gauge symmetry emerges naturally

Potential connection to electromagnetism

Abstract

Using complexified quaternions, a formalism without Lorentz frames, and therefore also without vierbeins, for dealing with tensor and spinor fields in curved spacetime is presented. A local U(1) gauge symmetry, which, it is speculated, might be related to electromagnetism, emerges naturally.