A general worldline quantum inequality

Details A general worldline quantum inequality A general worldline quantum inequality

1999-10-18

arxiv.org/abs/gr-qc/9910060v2

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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