The Dirac equation in general relativity, a guide for calculations

TL;DR

This paper provides an accessible overview of methods for solving the Dirac equation in curved spacetime, clarifying conventions and including examples to aid graduate students and researchers.

Contribution

It offers a comprehensive, clarified guide to calculations involving the Dirac equation in general relativity, with detailed examples and conventions.

Findings

Clarifies different approaches and conventions used in Dirac equation calculations in curved spacetime.

Includes practical examples from textbooks and literature.

Provides foundational material to assist graduate students and researchers.

Abstract

In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by including several examples from textbooks and the existing literature. In addition some basic material has been included in the appendices. It is our hope that graduate students and other re- searchers will find these notes useful.