We derive a McBryan-Spencer bound to the correlation function of a
one-dimensional array of quantum rotators in the Villain approximation of the
cosine interaction. We obtain the partition function of the system in the gas
representation and establish a lower bound on the external charge correlation
function. We also discuss the possible existence of a Kosterlitz-Thouless phase
for the quantum rotator in the Villain approximation.Comment: Latex 7 page
