An explicit quantum weak energy inequality for Dirac fields in curved spacetimes

TL;DR

This paper derives an explicit quantum weak energy inequality for Dirac fields in curved spacetimes, providing a clear bound that simplifies in static cases and aligns with known results in Minkowski spacetime.

Contribution

It offers a simplified, explicit derivation of a QWEI for Dirac fields, improving upon previous implicit bounds and confirming compatibility with local covariance.

Findings

Explicit QWEI bound for Dirac fields in curved spacetimes

Simplified bound for static curves in static spacetimes

Consistency with known Minkowski spacetime results

Abstract

The quantized Dirac field is known, by a result of Fewster and Verch, to satisfy a Quantum Weak Energy Inequality (QWEI) on its averaged energy density along time-like curves in arbitrary four-dimensional globally hyperbolic spacetimes. However, this result does not provide an explicit form for the bound. By adapting ideas from the earlier work, we give a simplified derivation of a QWEI for the Dirac field leading to an explicit bound. The bound simplifies further in the case of static curves in static spacetimes, and, in particular, coincides with a result of Fewster and Mistry in four-dimensional Minkowski spacetime. We also show that our QWEI is compatible with local covariance and derive a simple consequence.