Transport theory beyond binary collisions

Abstract

Using the Schwinger-Keldysh technique, we derive the transport equations for a system of quantum scalar fields. We first discuss the general structure of the equations and then their collision terms. Taking into account up to three-loop diagrams in φ 3 model and up to four-loop diagrams in φ 4 model, we obtain transport equations which include the contributions of multi-particle collisions and particle production processes, in addition to mean-field effects and binary interactions.

All orders Boltzmann collision term from the multiple scattering expansion of the self-energy

“…Since there are many excellent papers and books on the subject (e.g. [16,25,26,27,28]), we do not attempt another derivation here. Instead we focus on the approximations and assumptions used in the derivation and the interpretations of the equation.…”

“…The notations and discussions in this section largely follow those in Ref. [16] (with a different i convention for propagators, however). The starting point is the following Lagrangian density for a real scalar field:…”

“…Then each of these thermal cut diagrams must be That these coefficients cannot be the usual Feynman diagrams is evident from the appearance of the cutting rule propagators in Eqs. (14)(15)(16)(17). Hence, the coefficients must correspond to the vacuum Cutkosky (cut) diagrams.…”

“…In a recent paper, Carrington and Mrówczyński [16] addressed the multiparticle interactions in kinetic theories starting from the Schwinger-Keldysh formulation of quantum field theory (see also Ref. [17]).…”

“…The goal of this paper is to generalize the results of [16] using a different method. Instead of using a perturbative expansion, we use the multiple scattering expansion of the self-energy described in Ref.…”