TL;DR
This paper investigates boundary terms at poles in the complex Langevin method, identifying conditions that affect its correctness and providing complete solutions for simple cases, with implications for more complex scenarios.
Contribution
It offers a detailed analysis of boundary terms at poles in the complex Langevin method, highlighting conditions for correctness and solving simple cases.
Findings
Boundary terms at poles can spoil the correctness of the complex Langevin method.
Complete solutions are provided for simple, paradigmatic cases.
Discussion of lessons and open problems for more general cases.
Abstract
We discuss the problem of possible boundary terms at poles of the drift in the complex Langevin method, which spoil correctness of the method. For the simplest, however paradigmatic cases we can find complete answers. Lessons for more generic cases as well as open mathematical problems are discussed.
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