The averaged null energy condition for general quantum field theories in two dimensions

TL;DR

This paper proves that the averaged null energy condition holds for a broad class of states in any two-dimensional local quantum field theory with a mass gap, based on standard assumptions about the energy-momentum tensor.

Contribution

It demonstrates the validity of the averaged null energy condition in 2D quantum field theories under minimal, generic assumptions, extending previous results.

Findings

Averaged null energy condition holds for dense, translationally invariant states.

The proof relies on properties of the energy-momentum tensor as a Wightman field.

Results apply to any 2D local QFT with a mass gap and suitable energy-momentum tensor.

Abstract

It is shown that the averaged null energy condition is fulfilled for a dense, translationally invariant set of vector states in any local quantum field theory in two-dimensional Minkowski spacetime whenever the theory has a mass gap and possesses an energy-momentum tensor. The latter is assumed to be a Wightman field which is local relative to the observables, generates locally the translations, is divergence-free, and energetically bounded. Thus the averaged null energy condition can be deduced from completely generic, standard assumptions for general quantum field theory in two-dimensional flat spacetime.