Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-03-26
J.Math.Phys. 44 (2003) 4480-4513
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
RevTex4, 29 pages, 1 figure
Scientific paper
10.1063/1.1602554
Quantum weak energy inequalities (QWEI) provide state-independent lower bounds on averages of the renormalised energy density of a quantum field. We derive QWEIs for the electromagnetic and massive spin-one fields in globally hyperbolic spacetimes whose Cauchy surfaces are compact and have trivial first homology group. These inequalities provide lower bounds on weighted averages of the renormalized energy density as ``measured'' along an arbitrary timelike trajectory, and are valid for arbitrary Hadamard states of the spin-one fields. The QWEI bound takes a particularly simple form for averaging along static trajectories in ultrastatic spacetimes; as specific examples we consider Minkowski space [in which case the topological restrictions may be dispensed with] and the static Einstein universe. A significant part of the paper is devoted to the definition and properties of Hadamard states of spin-one fields in curved spacetimes, particularly with regard to their microlocal behaviour.
Fewster Christopher J.
Pfenning Michael J.
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