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

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.

24 pages, 0 figures

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• The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor
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• Quantum energy inequalities and local covariance II: Categorical formulation
• Quantum Energy Inequality for the Massive Ising Model
• Remarks on the Reeh-Schlieder property for higher spin free fields on curved spacetimes
• A semiclassical singularity theorem
• Quantum Inequalities from Operator Product Expansions
• A rigorous geometric derivation of the chiral anomaly in curved backgrounds
• An absolute quantum energy inequality for the Dirac field in curved spacetime
• Quantum Energy Inequalities in Pre-Metric Electrodynamics
• Wormhole restrictions from quantum energy inequalities
• Numerical results on Quantum Energy Inequalities in Integrable Models at the Two-Particle level
• A Quantum Energy Inequality for a Non-commutative QFT