Quantum Energy Inequalities along stationary worldlines
arXiv:2301.01698 · doi:10.1088/1361-6382/ace233
Abstract
Quantum energy inequalities (QEIs) are lower bounds on the averaged energy density of a quantum field. They have been proved for various field theories in general curved spacetimes but the explicit lower bound is not easily calculated in closed form. In this paper we study QEIs for the massless minimally coupled scalar field in four-dimensional Minkowski spacetime along stationary worldlines - curves whose velocity evolves under a 1-parameter Lorentz subgroup -- and find closed expressions for the QEI bound, in terms of curvature invariants of the worldline. Our general results are illustrated by specific computations for the six protoypical stationary worldlines. When the averaging period is taken to infinity, the QEI bound is consistent with a constant energy density along the worldline. For inertial and uniformly linearly accelerated worldlines, this constant value is attained by the Minkowski and Rindler vacuums respectively. It is an open question as to whether the bounds for other stationary worldlines are attained by other states of interest.
27 pages, 1 figure. v2 29 pages, 1 figure - additional commentary and references added. Final version to appear in Class Q Grav
References in corpus (6)
- Absolute quantum energy inequalities in curved spacetime
- Quantum energy inequalities and local covariance II: Categorical formulation
- Quantum inequality in spacetimes with small curvature
- A semiclassical singularity theorem
- A quantum energy inequality in the Sine--Gordon model
- Quantum inequality for a scalar field with a background potential