Time evolution of the decay process of unstable particles is investigated in
field theory models. We first formulate how to renormalize the non-decay
amplitude beyond perturbation theory and then discuss short-time behavior of
very long-lived particles. Two different formalisms, one that does and one that
does not, assume existence of the asymptotic field of unstable particles are
considered. The non-decay amplitude is then calculated by introducing a finite
time resolution of measurement, which makes it possible to discuss both
renormalizable and non-renormalizable decay interaction including the nucleon
decay. In ordinary circumstances the onset of the exponential decay law starts
at times as early as at roughly the resolution time, but with an enhanced
amplitude which may be measurable. It is confirmed that the short-time formula
1−Γt of the exponential decay law may be used to set limits on the
nucleon decay rate in underground experiments. On the other hand, an
exceptional example of S-wave decay of very small Q-value is found, which does
not have the exponential period at all.Comment: 26 pages, LATEX file with 8 PS figure
