Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-10-18
Class.Quant.Grav. 17 (2000) 1897-1911
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19pp, LaTeX2e. The statement of the main result is changed slightly. Several typos fixed, references added. To appear in Class
Scientific paper
10.1088/0264-9381/17/9/302
Worldline quantum inequalities provide lower bounds on weighted averages of the renormalised energy density of a quantum field along the worldline of an observer. In the context of real, linear scalar field theory on an arbitrary globally hyperbolic spacetime, we establish a worldline quantum inequality on the normal ordered energy density, valid for arbitrary smooth timelike trajectories of the observer, arbitrary smooth compactly supported weight functions and arbitrary Hadamard quantum states. Normal ordering is performed relative to an arbitrary choice of Hadamard reference state. The inequality obtained generalises a previous result derived for static trajectories in a static spacetime. The underlying argument is straightforward and is made rigorous using the techniques of microlocal analysis. In particular, an important role is played by the characterisation of Hadamard states in terms of the microlocal spectral condition. We also give a compact form of our result for stationary trajectories in a stationary spacetime.
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