| Abstract: |
| I will present recent progress on the forward-backward SDE (FBSDE) approach to Euclidean quantum field theories (EQFT), focusing on the example of the sine-Gordon model. The FBSDE describes the dynamics of transitioning between scales and can be viewed as a rigorous implementation of the renormalization group for the model, providing a powerful description of the interacting theory as a coupling with the Gaussian free field. Once established, the FBSDE is the starting point for a stochastic analysis of the EQFT to derive additional properties of the field, such as large deviations, decay of correlations, singularity, and a full verification of the Osterwalder-Schrader Axioms. I will outline the general construction of the stable reformulation and discuss ongoing work on the sine-Gordon model. |
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