Transition rate for process involving particles with high momentum in a plasma and infrared physics for QED plasma

We derive a formula for computing the transition rate for a process involving particles with momentum much higher than the temperature and chemical potentials in a plasma by using an effective field theory approach. We apply it to collision of charged particles with hard momentum inside a QED plasma. The Debye screening effect and the damping of a charged particle moving in QED plasma are studied. Using the Bloch-Nordsieck resummation, the infrared divergences due to the absence of magnetic screening for QED plasma are shown not to appear in physically measurable rates. The soft plasmon absorption and emission for charged particles are discussed.