2001/06/15 by C. Bérnard, Claude Bernard, Van M. Savage · 3 citations
Mathematics · Physics and Astronomy · #Field (mathematics) #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum field theory #Quantum mechanics #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevd.64.085010
published as Phys.Rev. D64 (2001) 085010 · 30 pages, 5 postscript figures
arxiv created 2001/06/15 · openalex publication_date 2001/09/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Many non-Hermitian but PT-symmetric theories are known to have a real positive spectrum. Since the action is complex for these theories, Monte Carlo methods do not apply. In this paper the first field-theoretic method for numerical simulations of PT-symmetric Hamiltonians is presented. The method is the complex Langevin equation, which was used previously to study complex Hamiltonians in statistical physics and in Minkowski space. We compute the equal-time one- and two-point Green's functions in zero and one dimension, where comparisons to known results can be made. The method should also be applicable in four-dimensional space-time. Our approach may also give insight into how to formulate a probabilistic interpretation of PT-symmetric theories.