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Quantum dynamics of Phi**4 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 $Φ^4$ 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 (BVA) and in the two-particle irreducible next-to-leading order large-N (2PI-1/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.