The Dirac equation in Rindler space: A pedagogical introduction

TL;DR

This paper provides a clear, pedagogical introduction to the Dirac equation in Rindler space, detailing derivations of spin connection coefficients, normalization procedures, and mode transformations relevant for quantum field theory in curved spacetime.

Contribution

It offers explicit derivations and simplified methods for understanding the Dirac equation in Rindler space, aiding students and researchers in quantum field theory in curved spacetime.

Findings

Explicit derivation of spin connection coefficients

Simplified normalization of states using Lagrange-Green identity

Derivation of Bogolubov coefficients relating Rindler and Minkowski modes

Abstract

A pedagogical introduction to the Dirac equation for massive particles in Rindler space is presented. The spin connection coefficients are explicitly derived using techniques from general relativity. We then apply the Lagrange-Green identity to greatly simplify calculation of the inner products needed to normalize the states. Finally, the Bogolubov coefficients relating the Rindler and Minkowski modes are derived in an intuitive manner. These derivations are useful for students interested in learning about quantum field theory in a curved space-time.