Nonequilibrium quantum fields in the large-Nexpansion

An effective action technique for the time evolution of a closed system consisting of one or more mean fields interacting with their quantum fluctuations is presented. By marrying large-N expansion methods to the Schwinger-Keldysh closed time path formulation of the quantum effective action, causality of the resulting equations of motion is ensured and a systematic, energy-conserving and gauge-invariant expansion about the quasiclassical mean field(s) in powers of 1/N developed. The general method is exposed in two specific examples, O(N) symmetric scalar λ${\mathrm{\Phi }}^4$ theory and quantum electrodynamics (QED) with N fermion fields. The λ${\mathrm{\Phi }}^4$ case is well suited to the numerical study of the real time dynamics of phase transitions characterized by a scalar order parameter. In QED the technique may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes in a relativistic ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$ plasma. A simple renormalization scheme that makes practical the numerical solution of the equations of motion of these and other field theories is described.