Quantum dynamics of Φ⁴ field theory beyond leading order in 1+1 dimensions

We consider the out-of-equilibrium evolution of a classical condensate field φ=〈Φ〉 and its quantum fluctuations for a Φ⁴ model in 1+1 dimensions with a double well potential. We use the two-particle point-irreducible (2PPI) formalism in the two-loop approximation. We compare our results to those obtained in the Hartree approximation, in the bare vertex approximation, and in the two-particle irreducible next-to-leading order large-N approach, with thermal initial conditions. In the 2PPI scheme, we find that the system tends to the symmetric configuration at late times, as expected in the absence of spontaneous symmetry breaking.