A microlocal approach to the stochastic nonlinear Dirac equation

30.01.2026, 11:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Beatrice Costeri (Pavia, IT)

We present a novel framework for the study of a wide class of nonlinear Fermionic stochastic partial differential equations of Dirac type, which is inspired by the functional approach to the λ Φ^3 model. The main merit is that, by realizing random spinor fields within a suitable algebra of functional-valued Dirac distributions, we are able to use specific techniques proper of microlocal analysis. These allow us to deal with renormalization using an Epstein-Glaser perspective, hence without resorting to any specific regularization scheme. As a concrete example we shall use this method to discuss the stochastic Thirring model in two Euclidean dimensions and we shall comment on its applicability to a larger class of Fermionic SPDEs.
Based on joint work with A. Bonicelli, C. Dappiaggi and P. Rinaldi -- Math.Phys.Anal.Geom. 27 (2024) 3, 16

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