Quantum dynamics ofΦ4field theory beyond leading order in1+1dimensions

Abstract

We consider the out-of-equilibrium evolution of a classical condensate field ϭ͗⌽͘ and its quantum fluctuations for a ⌽ 4 model in 1ϩ1 dimensions with a double well potential. We use the two-particle pointirreducible ͑2PPI͒ 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.

Out-of-equilibrium evolution of quantum fields in the hybrid model with quantum back reaction

“…This formalism has also been used beyond these mean field approaches [28,30,49,50,51]. As an alternative approach beyond leading orders we have recently adapted [23,24] the so-called two-particle point irreducible (2PPI) formalism [22,52] to nonequilibrium quantum field theory.…”

“…This sunset graph leads to time integrations over the past of classical and quantum fields ("memory integrations") and introduces scattering of the quanta (see Ref. [23,24] for two-loop simulations of Φ 4 theory in 1+1 dimensions). While it would be interesting to study how this next-to-leading order diagram affects the dynamics studied here, this is beyond the scope of this work.…”

“…(ii) on the formal level we present a consistent renormalization of the gap equations arising in the Hartree approximation, making use of the two-particle pointirreducible (2PPI) formalism [22,23,24]. This is a first example of renormalization for coupled channel system out of equilibrium with Hartree-type self-interaction, and goes beyond the one-loop renormalization of Ref.…”

Two-particle irreducible finite temperature effective potential of theO(N)linear sigma model in1+1dimensions at next-to-leading order ofBaacke1, Michalski2 2004Phys. Rev. DSelf Cite

“…Coming back to the simulations in 1 + 1 dimensions for the case N = 1 [28,30] spontaneous symmetry breaking was found in the late time behavior of the Hartree approximation, whereas in both the 2PI and the 2PPI the mean field approaches the symmetric phase at late times. In contrast to that, the 2PPI approximation in equilibrium displays spontaneous symmetry breaking, and so does the 2PI approximation both with correct N = 1 combinatorics and with 1/N combinatorics [38].…”

“…A comparison [28,30] of various approximations for the O(1) model, i.e., a model with a simple double-well potential, has displayed some still not well-understood features. The O(1) model has thermal kink transitions [31,32,33,34] that lead to a symmetric phase in the exact theory.…”