Vacuum Energy Decay

The problem of the vacuum energy decay is studied through the analysis of the vacuum survival amplitude $\mathcal{A}(z,z^{\mathrm{\prime }})$. Transition amplitudes are computed for finite time-span, $Z\equiv z^{\mathrm{\prime }}-z$, and their {\em late time} behavior is discussed up to first order in the coupling constant, $\text{l}$.