The time evolution of a quantum system in field theory is studied. We use the Shibata-Hashitsume projection operator method, which is a nonperturbative expansion method known in quantum mechanics. We calculate the time evolution of expectation values of creation and annihilation operators in a super-renormalizable model with unstable particles (or resonances) and study the initial temperature dependence. We carry out the renormalization of the ultraviolet divergence that appears in the time-dependent frequency shift using a mass counterterm. A harmless divergence of the lnt-type remains at the initial time t = 0 after mass renormalization. It is suggested that the Shibata-Hashitsume projection operator method is applicable to quantum field theory.
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