Quantum inequality for a scalar field with a background potential

TL;DR

This paper derives first-order quantum inequality bounds for a scalar field with a spacetime-varying mass in Minkowski space, providing tools to analyze exotic spacetimes in general relativity.

Contribution

It introduces a perturbative approach to quantum inequalities for scalar fields with background potentials, extending previous results to more general settings.

Findings

Explicit first-order correction formulas derived

Bounds expressed in terms of potential and derivatives

Techniques applicable to small-curvature spacetimes

Abstract

Quantum inequalities are bounds on negative time-averages of the energy density of a quantum field. They can be used to rule out exotic spacetimes in general relativity. We study quantum inequalities for a scalar field with a background potential (i.e., a mass that varies with spacetime position) in Minkowski space. We treat the potential as a perturbation and explicitly calculate the first-order correction to a quantum inequality with an arbitrary sampling function, using general results of Fewster and Smith. For an arbitrary potential, we give bounds on the correction in terms of the maximum values of the potential and its first three derivatives. The techniques we develop here will also be applicable to quantum inequalities in general spacetimes with small curvature, which are necessary to rule out exotic phenomena.