We derive the nonequilibrium real-time evolution of an $O\left(N\right)\mathrm{}$-invariant scalar quantum field theory in the presence of a nonvanishing expectation value of the quantum field. Using a systematic $1/N$ expansion of the 2PI effective action to next-to-leading order, we obtain nonperturbative evolution equations which include scattering and memory effects. The equivalence of the direct method, which requires the resummation of an infinite number of skeleton diagrams, with the auxiliary-field formalism, which involves only one diagram at next-to-leading order, is shown.

• Received 6 February 2002

DOI:https://doi.org/10.1103/PhysRevD.66.045008