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

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Abstract
It is shown that in any local quantum field theory in two-dimensional Minkowski space–time possessing a mass gap and an energy-momentum tensor, the averaged null energy condition is fulfilled for the set of those vector states which correspond to energetically strongly damped, local excitations of the vacuum. This set of physical vector states is translation invariant and dense. The energy-momentum tensor of the theory 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 space–time.
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