Exact Results in Quantum Theory
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2021-03-19 (14:15) 
Paweł Duch (Universitaet Leipzig)
Renormalization of the stochastic quantization equation of the Phi^4_3 model with the use of the Polchinski flow equation
Stochastic quantization is a method of constructing models of Euclidean quantum field theory with the use of stochastic partial differential equations driven by a random force called the white noise. Stochastic quantization equations of nontrivial QFT models are typically ill-posed. They require renormalization and admit only distributional solutions. A general solution theory for such equations was developed only recently by Martin Hairer. His breakthrough work triggered much interest in singular stochastic PDEs in the mathematical community and was awarded the Fields Medal in 2014.
In the first part of the talk, I will give a short introduction to the stochastic quantization technique. In the second part, I will outline a new method of constructing solutions of singular stochastic PDEs. I will illustrate the method with the example of the stochastic quantization equation of the Phi^4 model in 3 dimensions. A distinctive feature of my construction is the use of the Wilsonian renormalization group theory and the Polchinski flow equation.
In the first part of the talk, I will give a short introduction to the stochastic quantization technique. In the second part, I will outline a new method of constructing solutions of singular stochastic PDEs. I will illustrate the method with the example of the stochastic quantization equation of the Phi^4 model in 3 dimensions. A distinctive feature of my construction is the use of the Wilsonian renormalization group theory and the Polchinski flow equation.