Stochastic Quantization of Exponential Quantum Field Theory

Explore a comprehensive lecture on the stochastic quantization of exponential quantum field theory, focusing on the two-dimensional scalar field with exponential interaction. Delve into the elliptic and parabolic Euclidean stochastic quantization of the Høegh-Krohn or Liouville model. Examine how this problem can be reduced to studying a random PDE with multiplicative noise given by the Wick exponential of the free Gaussian field. Investigate the properties of the distribution :e^(βΨ):, comparing it to Wick powers and Wick trigonometric functions, and learn about its Besov regularity. Gain insights from the joint work of Sergio Albeverio, Francesco C. De Vecchi, and Massimiliano Gubinelli on the elliptic stochastic quantization of two-dimensional Euclidean QFTs.