A note on symmetries in the path integral formulation of the Langevin dynamics
arXiv:1703.08192 · doi:10.1103/PhysRevE.98.042140
Abstract
We study a dissipative Langevin dynamics in the path integral formulation using the Martin-Siggia-Rose formalism. The effective action is supersymmetric and we identify the supercharges. In addition we study the transformations generated by superderivatives, which were recently included in the cohomological structure emerging in the dissipative systems. We find that these transformations do not generate Ward identities, which are explicitly broken, however, they lead to universal identities, which we derive from Schwinger-Dyson equations. We confirm that the above identities hold in an explicit example of Ornstein-Uhlenbeck process.
arXiv comment13 pages, the manuscript completely re-written as we verified that the breaking of some of the identities was erroneously attributed to anomaly that is indeed not present
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