A short remark on negative energy densities and quantum inequalities

TL;DR

This paper discusses the limitations of quantum inequalities in quantum field theory, providing an example where no lower bound on the weighted average of negative energy density exists, challenging previous assumptions.

Contribution

It presents an explicit example of a sampling function that violates the quantum inequality, highlighting potential exceptions in the theory.

Findings

Existence of sampling functions without quantum inequalities

Negative energy densities can be unbounded in certain cases

Challenges to the universality of quantum inequalities

Abstract

In quantum field theory it is generally known that the energy density may be negative at a given point in spacetime. A number of papers have shown that there is a restriction on this energy density which is called a quantum inequality (QI). A QI is the lower bound to the "weighted average" of the energy density at a given point integrated over a time dependent sampling function. In this paper we give an example of a sampling function for which there is no QI.