2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58330We 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.Latex 7 pagesMathematical Physicstext