Complex Langevin Equations and Schwinger-Dyson Equations
Gerald Guralnik, Cengiz Pehlevan
TL;DR
This paper explores the connection between complex Langevin equations and Schwinger-Dyson equations, demonstrating that stationary distributions of the former correspond to solutions of the latter in quantum field theory, with examples and implications discussed.
Contribution
It establishes a theoretical link between complex Langevin dynamics and Schwinger-Dyson equations, providing new insights into quantum field theory phase space analysis.
Findings
Stationary distributions of complex Langevin equations solve Schwinger-Dyson equations.
Examples provided in zero dimensions and lattice models.
Discussion on relevance to quantum field theory phase space.
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.
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