Quantum field dynamics of the slow rollover in the linear delta expansion

We show how the linear delta expansion, as applied to the slow-roll transition in quantum mechanics, can be recast in the closed time-path formalism. This results in simpler, explicit expressions than were obtained in the Schrödinger formulation and allows for a straightforward generalization to higher dimensions. Motivated by the success of the method in the quantummechanical problem, where it has been shown to give more accurate results for longer than existing alternatives, we apply the linear delta expansion to four-dimensional field theory. At small times all methods agree. At later times, the first-order linear delta expansion is consistently higher that Hartree-Fock, but does not show any sign of a turnover. A turnover emerges in second-order of the method, but the value of 〈Φ̂(t)〉 at the turnover is larger that that given by the Hartree-Fock approximation. Based on this calculation, and our experience in the corresponding quantum-mechanical problem, we believe that the Hartree-Fock approximation does indeed underestimate the value of 〈Φ̂(t)〉 at the turnover. In subsequent applications of the method we hope to implement the calculation in the context of an expanding universe, following the line of earlier calculations by Boyanovsky et al., who used the Hartree-Fock and large-N methods. It seems clear, however, that the method will become unreliable as the system enters the reheating stage.