  Production of electron-positron pairs with invariant masses less than 300 MeV
from thermalized hadronic matter in relativistic heavy ion collisions is
calculated using a soft virtual photon approximation. The general theoretical
framework is reviewed and extended to include arbitrarily massed and charged
reaction partners, which we apply to pions and quarks. This result, exact
within the soft photon approximation, is compared with a widely used
approximate result which uses an electromagnetic amplitude limited in validity
to momentum transfers less than $4m_{\pi(q)}^{2}$. A comparison is made between
the rate of production of zero total momentum soft dileptons obtained using
resummation techniques in QCD perturbation theory to that which we calculate
using this soft photon approximation.
