Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-08-19
J.Phys.A41:025402,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23pp. Minor corrections and clarifications added
Scientific paper
10.1088/1751-8113/41/2/025402
In this paper we discuss local averages of the energy density for the non-minimally coupled scalar quantum field, extending a previous investigation of the classical field. By an explicit example, we show that such averages are unbounded from below on the class of Hadamard states. This contrasts with the minimally coupled field, which obeys a state-independent lower bound known as a Quantum Energy Inequality (QEI). Nonetheless, we derive a generalised QEI for the non-minimally coupled scalar field, in which the lower bound is permitted to be state-dependent. This result applies to general globally hyperbolic curved spacetimes for coupling constants in the range $0<\xi\leq 1/4$. We analyse the state-dependence of our QEI in four-dimensional Minkowski space and show that it is a nontrivial restriction on the averaged energy density in the sense that the lower bound is of lower order, in energetic terms, than the averaged energy density itself.
Fewster Christopher J.
Osterbrink Lutz W.
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