  We generalize a result of Vollick constraining the possible behaviors of the
renormalized expected stress-energy tensor of a free massless scalar field in
two dimensional spacetimes that are globally conformal to Minkowski spacetime.
Vollick derived a lower bound for the energy density measured by a static
observer in a static spacetime, averaged with respect to the observers proper
time by integrating against a smearing function. Here we extend the result to
arbitrary curves in non-static spacetimes. The proof, like Vollick's proof, is
based on conformal transformations and the use of our earlier optimal bound in
flat Minkowski spacetime. The existence of such a quantum inequality was
previously established by Fewster.
