Considering the propagation of off-shell particles in the framework of
thermal held theory, we present the general formalism for the calcula
tion of the production rate of soft photons and dileptons from a hot p
lasma. This approach is first illustrated with an electrodynamic plasm
a. The photon production rate from strongly interacting quarks in the
quark-gluon plasma, which might be formed in ultrarelativistic heavy i
on collisions, is also calculated. We utilize an effective field theor
y incorporating dynamical chiral symmetry breaking and obtain results
in the previously inaccessible regime of photon energies of the order
of the plasma temperature.