Schwinger-Dyson equations and line integrals

The complex Langevin (CL) method sometimes shows convergence to the wrong limit, even though the Schwinger-Dyson equations (SDE) are fulfilled. We analyze this problem in a more general context for the case of one complex variable. We prove a theorem that shows that under rather general conditions n...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2019-01, Vol.52 (3), p.35201
Main Authors: Salcedo, Lorenzo Luis, Seiler, Erhard
Format: Article
Language:English
Subjects:
complex Langevin
Schwinger-Dyson equations
sign problem
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Summary:The complex Langevin (CL) method sometimes shows convergence to the wrong limit, even though the Schwinger-Dyson equations (SDE) are fulfilled. We analyze this problem in a more general context for the case of one complex variable. We prove a theorem that shows that under rather general conditions not only the equilibrium measure of CL but any linear functional satisfying the SDE on a space of test functions is given by a linear combination of integrals along paths connecting the zeroes of the underlying measure and noncontractible closed paths. This proves rigorously a conjecture stated long ago by one of us (L. L. S.) and explains a fact observed in nonergodic cases of CL.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aaefca