Constraints on Spatial distributions of Negative Energy

TL;DR

This paper explores the constraints on how negative energy density can be spatially distributed in quantum field theory, reviewing known energy conditions and constructing explicit examples of allowed distributions.

Contribution

It introduces a systematic study of spatial distributions of negative energy, combining known restrictions with new geometric constraints and explicit distribution examples.

Findings

Certain geometric configurations of negative energy are ruled out or constrained.

Explicit examples of permissible negative energy distributions are constructed.

Spacetime averaged quantum inequalities in two dimensions are discussed.

Abstract

This paper initiates a program which seeks to study the allowed spatial distributions of negative energy density in quantum field theory. Here we deal with free fields in Minkowski spacetime. Known restrictions on time integrals of the energy density along geodesics, the averaged weak energy condition and quantum inequalities are reviewed. These restrictions are then used to discuss some possible constraints on the allowable spatial distributions of negative energy. We show how some geometric configurations can either be ruled out or else constrained. We also construct some explicit examples of allowed distributions. Several issues related to the allowable spatial distributions are also discussed. These include spacetime averaged quantum inequalities in two-dimensional spacetime, the failure of generalizations of the averaged weak energy condition to piecewise geodesics, and the issue of when the local energy density is negative in the frame of all observers.