2024/01/24 by Massimiliano Gubinelli, Sarah-Jean Meyer, Gubinelli, Massimiliano +1 · 1 citation
Physics and Astronomy · Mathematics · Economics, Econometrics and Finance · #Black Holes and Theoretical Physics #Numerical methods for differential equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2401.13648
We develop a stochastic analysis of the sine-Gordon Euclidean quantum field (cos (βφ))2 on the full space up to the second threshold, i.e. for β2 < 6 π. The basis of our method is a forward-backward stochastic differential equation (FBSDE) for a decomposition (Xt)t \geqslant 0 of the interacting Euclidean field X∞ along a scale parameter t \geqslant 0. This FBSDE describes the optimiser of the stochastic control representation of the Euclidean QFT introduced by Barashkov and one of the authors. We show that the FBSDE provides a description of the interacting field without cut-offs and that it can be used effectively to study the sine-Gordon measure to obtain results about large deviations, integrability, decay of correlations for local observables, singularity with respect to the free field, Osterwalder-Schrader axioms and other properties.