The averaged null energy condition and difference inequalities in quantum field theory

TL;DR

This paper proves the difference inequality for a massless scalar field in 2D spacetime, showing that subtracting Casimir-vacuum contributions restores the averaged null energy condition in quantum field theory.

Contribution

It provides a proof of the difference inequality in 2D quantum field theory, extending the understanding of energy conditions beyond classical limits.

Findings

Proved the difference inequality for a massless scalar in 2D spacetime.

Demonstrated that subtracting Casimir-vacuum contributions satisfies ANEC.

Extended the theoretical framework of quantum energy conditions.

Abstract

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.