  In-medium interactions of a particle in a hot plasma are considered in the
framework of thermal field theory. The formalism to calculate gauge invariant
rates for photon and dilepton production from the medium is given. In the
application to a QED plasma, astrophysical consequences are pointed out. The
photon production rate from strongly interacting quarks in the quark--gluon
plasma, which might be formed in ultrarelativistic heavy ion collisions, is
calculated in the previously unaccessible regime of photon energies of the
order of the plasma temperature. For temperatures below the chiral phase
transition, an effective field theory incorporating dynamical chiral symmetry
breaking is employed, and perturbative QCD at higher temperatures. A smooth
transition between both regions is obtained. The relevance to the soft photon
problem and to high energy heavy ion experiments is discussed.
