Complex Langevin Equations and Schwinger-Dyson Equations

Abstract

Stationary distributions of complex Langevin equations are shown to be the complexified path integral solutions of the Schwinger-Dyson equations of the associated quantum field theory. Specific examples in zero dimensions and on a lattice are given. Relevance to the study of quantum field theory phase space is discussed.

23 pages, 4 figures, elsart, typos fixed, includes additional content

References in corpus (13)

• Lattice simulations of real-time quantum fields
• Stochastic quantization at finite chemical potential
• Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
• Real-time gauge theory simulations from stochastic quantization with optimized updating
• Real-time gauge theory simulations from stochastic quantization using optimized updating
• Representation of Complex Probabilities
• Complex Probabilities on R^N as Real Probabilities on C^N and an Application to Path Integrals
• Numerical Simulations of PT-Symmetric Quantum Field Theories
• Theta Vacua and Boundary Conditions of the Schwinger Dyson Equations
• The Mechanism of Complex Langevin Simulations
• Existence of positive representations for complex weights
• On the Correct Convergence of Complex Langevin Simulations for Polynomial Actions
• Mollifying Quantum Field Theory or Lattice QFT in Minkowski Spacetime and Symmetry Breaking

Cited by in corpus (37)

• The Complex Langevin method: When can it be trusted?
• Complex Langevin: Etiology and Diagnostics of its Main Problem
• Simulating full QCD at nonzero density using the complex Langevin equation
• Gauge cooling in complex Langevin for QCD with heavy quarks
• Adaptive stepsize and instabilities in complex Langevin dynamics
• Some remarks on Lefschetz thimbles and complex Langevin dynamics
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• Complex Langevin and boundary terms
• Localised distributions and criteria for correctness in complex Langevin dynamics
• Does the complex Langevin method give unbiased results?
• Complex saddle points and the sign problem in complex Langevin simulation
• Complex Langevin simulations and the QCD phase diagram: Recent developments
• Effective Potential for Complex Langevin Equations
• Infinitely many inequivalent field theories from one Lagrangian
• Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel
• Complex Langevin Simulations of Zero-dimensional Supersymmetric Quantum Field Theories
• Complex Langevin Dynamics in Large $N$ Unitary Matrix Models
• Gibbs sampling of complex valued distributions
• Temporal breakdown and Borel resummation in the complex Langevin method
• Schwinger-Dyson equations and line integrals
• Theory Including Future Not Excluded -- Formulation of Complex Action Theory II --
• Quantum field theories on the Lefschetz thimble
• Stochastic Quantization for Complex Actions
• Fermion Bag Approach for Massive Thirring Model at Finite Density
• Complex Langevin Dynamics and Supersymmetric Quantum Mechanics
• Exact Statistics of Chaotic Dynamical Systems
• The Lefschetz thimble and the sign problem
• Extending complex Langevin simulations to full QCD at nonzero density
• Stochastic Quantization of Real-Time Thermal Field Theory
• The Role of Integration Cycles in Complex Langevin Simulations
• A new look at the Helmholtz equation: Lefschetz thimbles and the einbein action
• Necessary and sufficient conditions for correctness of complex Langevin
• Momentum relation and classical limit in the future-not-included complex action theory
• Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking
• Correctness criteria for complex Langevin
• Linearized renormalization