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

S P Dawson·C J Fewster
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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.

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S P Dawson, C J Fewster. 2006-10-31. An explicit quantum weak energy inequality for Dirac fields in curved spacetimes. https://doi.org/10.1088/0264-9381%2F23%2F23%2F005

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