  Medium-induced modifications of the pion and quark-antiquark annihilation
mechanisms of dilepton production during relativistic heavy ion collisions are
considered. Due to the dense hadron environment, the pions produced during a
collision are effectively confined in a finite volume, in which they live for a
finite time which is scaled as the lifetime of a fireball. Our results indicate
that, due to the space-time finiteness of the pion system which generates the
corresponding quantum randomization, the dilepton rates are finite in the
invariant low-mass region M<2m_\pi. It is found that the spatial finiteness of
quark wave functions and the finiteness of the lifetime of excited states
result in the same effect for the quark-antiquark annihilation to dileptons.
The breaking of the detailed energy-momentum conservation due to the broken
translation invariance is discussed.
