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We use a Magnus approximation at the level of the equations ofmotion for a harmonic system with a time-dependent frequency,to find an expansion for its in?out effective action, and a unitaryexpansion for the Bogoliubov transformation between in and outstates. The dissipative effects derived therefrom are comparedwith the ones obtained from perturbation theory in powers of thetime-dependent piece in the frequency, and with those derived us-ing multiple scale analysis in systems with parametric resonance.We also apply the Magnus expansion to the in?in effective action,to construct reality and causal equations of motion for the externalsystem. We show that the nonlocal equations of motion can bewritten in terms of a ??retarded Fourier transform?? evaluated at theresonant frequency.