SMuK 2023 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantum Field Theory II

MP 3.1: Hauptvortrag

Dienstag, 21. März 2023, 11:00–11:30, HSZ/0304

Renormalization of singular stochastic partial differential equations — •Pawel Duch — Adam Mickiewicz University, Poznan, Poland

Stochastic PDEs, i.e. partial differential equation with random terms or coefficient, play an important role in mathematical physics and have applications in areas such as quantum field theory, statistical mechanics and material science. Well-known examples of stochastic PDEs are the KPZ equation describing the motion of a growing interface or the stochastic quantization equation of the Φ⁴ Euclidean QFT. Most of the interesting non-linear stochastic PDEs, including the ones mentioned above, are too singular to admit classical treatment. Solving such equations poses a formidable challenge and usually requires the regularization and renormalization of the equation.

After giving a brief overview of the tremendous progress in the area of singular stochastic PDEs in the past decade, I will present a novel approach to such PDEs proposed in my recent work. The approach uses the framework of the Wilsonian renormalization group theory and is based on a certain flow equation that plays an analogous role to the Polchinski equation in QFT. The approach allows to solve a large class of singular stochastic PDEs in a systematic manner and avoids algebraic and combinatorial problems arising in different approaches.