2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55373We study the time development of correlation functions at both zero and finite temperature with Shibata-Hashitsume's projection operator method and carry out the renormalization of ultraviolet divergence that appears in a time-dependent frequency shift, using a mass counter term. A harmless divergence of log t-type remains at an initial time t=0 after the lowest order renormalization.9 pages, 4 figures, RevTeXHigh Energy Physics - TheoryNuclear TheoryQuantum Physicstext