Dynamics of broken symmetry λφ⁴ field theory

We study the domain of validity of a Schwinger-Dyson approach to nonequilibrium dynamics when 〈φ(x)〉≠0. We perform exact numerical simulations of the one- and two-point functions of a single component λφ⁴ field theory in 1+1 dimensions in the classical field theory case. We compare these results to two self-consistent truncations of the Schwinger-Dyson equations which ignore three-point vertex function corrections. The first approximation, which we called the bare vertex approximation, sets the three-point function to one. It gives a promising description for 〈φ(x)〉=φ(t). The second approximation, which ignores higher in 1/N corrections to the 2PI generating functional is not as accurate for φ(t) for the case N=1. Both approximations have serious deficiencies in describing the two-point function when φ(0)≳0.4.