  We discuss decay of unstable particles and pair annihilation of stable heavy
particles that occur in the cosmic medium, from the point of the fundamental
microscopic theory. A fully quantum mechanical treatment shows that the effect
of thermal environment on these processes cannot be described in terms of
quantities on the mass shell alone, thus requiring an extention of the
Boltzmann-like equation. The off-shell effect tends to prolong physical
processes that take place subsequent to the decay.
