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We present an operator definition of the collisional energy and momentum losssuffered by an energetic charged particle in the presence of a medium. Ourapproach uses the energy-momentum tensor of the medium to evaluate the energyand momentum transfer rates. We apply this formalism to an energetic lepton orquark propagating in thermal electron-positron or quark-gluon plasmas,respectively. By using two different approaches to describe the energeticcharged particle, an external current approach and a diagrammatic approach, weshow explicitly that the operator method reproduces the known results forcollisional energy loss from the scattering rate formalism. We further use ourresults to evaluate the collisional energy and momentum loss for the cases ofheavy quark propagation through a quark-gluon plasma and energetic muonpropagation in an electron-positron plasma produced in a high-intensity laserfield.

An operator definition and derivation of collisional energy and momentum loss in relativistic plasmas