Restricted phase-space approximation in real-time stochastic quantization

Abstract

We perform and extend real-time numerical simulation of a low-dimensional scalar field theory or a quantum mechanical system using stochastic quantization. After a brief review of the quantization method and the complex Langevin dynamics, we calculate the propagator and make a comparison with analytical results. This is a first step toward general applications, and we focus only on the vacuum properties of the theory; this enables us to handle the boundary condition with the $i\epsilon$ prescription in frequency space. While we can control stability of the numerical simulation for any coupling strength, our results turn out to flow into an unphysical fixed-point, which is qualitatively understood from the corresponding Fokker-Planck equation. We propose a simple truncation scheme, "restricted phase-space approximation," to avoid the unphysical fixed-point. With this method, we obtain stable results at reasonably good accuracy. Finally we give a short discussion on the closed-time path formalism and demonstrate the direct computation of the vacuum expectation value not with the $i\epsilon$ prescription but from an explicit construction of the Feynman kernel.

35 pages, 10 figures; typos corrected, irrelevant numerical tests deleted, confusing explanations elaborated, sections sorted out well; main results not changed

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Cited by in corpus (11)

• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: a comparison with multi-parameter reweighting
• Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method
• Evolution to the Quark-Gluon Plasma
• The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant
• Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Stochastic quantization and diffusion models
• A Phase Prediction Method for Pattern Formation in Time-Dependent Ginzburg-Landau Dynamics for Kinetic Ising Model without a priori Assumptions on Domain Patterns
• Classical Statistical simulation of Quantum Field Theory
• Correlation Functions and Stochastic Feynman Rules for Self-Interacting Scalar Fields