Convergence results in the stochastic sine-Gordon model: an algebraic viewpoint

26.04.2024, 11:00 Uhr  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Alberto Bonicelli (Pavia, Italy)

The importance of the sine-Gordon model in 1+1 spacetime dimensions resides in the integrability of the field theory that it describes. A recent result showed how, within the setting of algebraic quantum field theory, this property translates into a convergence result for both the formal series associated to the S-matrix and to the interacting field of the quantum field theory.

After introducing an algebraic approach to the perturbative study of singular stochastic PDEs, I will show how an adaptation of the aforementioned convergence results yields convergence of the momenta of the solution to a stochastic version of the sine-Gordon equation. Interestingly enough, our two-step procedure passes through the quantum theory and recollects the stochastic information via the classical limit.