Id. Lawrie et Db. Mckernan, NONEQUILIBRIUM PERTURBATION-THEORY FOR COMPLEX SCALAR FIELDS, Physical review. D. Particles and fields, 55(4), 1997, pp. 2290-2297
Real-time perturbation theory is formulated for complex scalar fields
away from thermal equilibrium in such a way that dissipative effects a
rising from the absorptive parts of loop diagrams are approximately re
summed into the unperturbed propagators. Low order calculations of phy
sical quantities then involve quasiparticle occupation numbers which e
volve with the changing state of the field system, in contrast with st
andard perturbation theory, where these occupation numbers are frozen
at their initial values. The evolution equation of the occupation numb
ers can be cast approximately in the form of a Boltzmann equation. Par
ticular attention is given to the effects of a nonzero chemical potent
ial, and it is found that the thermal masses and decay widths of quasi
particle modes are different for particles and antiparticles.