Lepton-pair production from a quark-gluon plasma to first order inαs

Lepton-pair production from a quark-gluon plasma is calculated to first order in ${\alpha }_s$. The full kinematic region is considered, i.e., also when the lepton pair is moving. The crossing symmetry at finite temperature is discussed for positive as well as negative values of $q^2$, the invariant mass of the lepton pair. The cancellation of collinear singularities and infrared divergences between the different contributions is explicitly shown. The final result is presented in the form of a well-defined double integral over energies of constitutents.