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A quantum weak energy inequality for spin-one fields in curved space-time

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JournalJournal of Mathematical Physics
DatePublished - Oct 2003
Issue number10
Volume44
Number of pages34
Pages (from-to)4480-4513
Original languageEnglish

Abstract

Quantum weak energy inequalities (QWEI) provide state-independent lower bounds on averages of the renormalized energy density of a quantum field. We derive QWEIs for the electromagnetic and massive spin-one fields in globally hyperbolic space-times 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 space-times; 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 space-times, particularly with regard to their microlocal behavior.(C) 2003 American Institute of Physics.

    Research areas

  • ROBERTSON-WALKER SPACETIMES, MASSIVE VECTOR-FIELDS, GENERAL-RELATIVITY, SINGULARITY STRUCTURE, HADAMARD CONDITION, 2-POINT FUNCTION, QUANTIZED FIELD, DIRAC FIELDS, WARP DRIVE, UNIVERSE

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