Operator definition and derivation of collisional energy and momentum loss in relativistic plasmas

We present an operator definition of the collisional energy and momentum loss suffered by an energetic charged particle in the presence of a medium. Our approach uses the energy-momentum tensor of the medium to evaluate the energy and momentum transfer rates. We apply this formalism to an energetic lepton or quark propagating in thermal electron-positron or quark-gluon plasmas, respectively. By using two different approaches to describe the energetic charged particle, an external current approach and a diagrammatic approach, we show explicitly that the operator method reproduces the known results for collisional energy loss from the scattering rate formalism. We further use our results to evaluate the collisional energy and momentum loss for the cases of heavy quark propagation through a quark-gluon plasma and energetic muon propagation in an electron-positron plasma produced in a high-intensity laser field.