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

It is shown that in any local quantum field theory in two-dimensional Minko wski space-time possessing a mass gap and an energy-momentum tensor, the av eraged null energy condition is fulfilled for the set of those vector state s which correspond to energetically strongly damped, local excitations of t he 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 tr anslations, is divergence-free, and energetically bounded. Thus the average d null energy condition can be deduced from completely generic, standard as sumptions for general quantum field theory in two-dimensional flat space-ti me. (C) 2000 American Institute of Physics. [S0022-2488(00)00701-5].