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arXiv · 1809.06888

Schwinger-Dyson equations and line integrals

Lorenzo Luis Salcedo·Erhard Seiler
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Abstract

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 us (L.~L.~S.) and explains a fact observed in nonergodic cases of CL. one us (L.~L.~S.) and explains a fact observed in nonergodic cases of CL.

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Lorenzo Luis Salcedo, Erhard Seiler. 2018-09-18. Schwinger-Dyson equations and line integrals. https://doi.org/10.1088/1751-8121%2Faaefca

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