A non-geometric representation of the Dirac equation in curved spacetime

TL;DR

This paper presents a novel approach to formulating the Dirac equation in curved spacetime by employing analytical PDE methods instead of traditional geometric techniques.

Contribution

It introduces a non-geometric representation of the Dirac equation, offering a new perspective for analyzing fermions in curved backgrounds.

Findings

Provides a PDE-based formulation of the Dirac equation in curved spacetime

Enables alternative analytical methods for studying fermions in gravitational fields

Potentially simplifies certain calculations in quantum field theory in curved spacetime

Abstract

We write the Dirac equation in curved 4-dimensional Lorentzian spacetime using concepts from the analysis of partial differential equations as opposed to geometric concepts.