AG Mathematische Physik, Azam Jahandideh (Poznan): Stochastic quantization of two-dimensional $P(\Phi)$ Quantum Field Theory

Azam Jahandideh (Poznan)

Stochastic quantization of two-dimensional $P(\Phi)$ Quantum Field Theory

Abstract:

We
give a simple and self-contained construction of the $P(\Phi$ Euclidean
Quantum Field Theory in the plane and verify the Osterwalder-Schrader
axioms: translational and rotational invariance, reflection positivity
and regularity. In the intermediate steps of the construction, we study
measures on spheres. In order to control the infinite volume limit, we
use the parabolic stochastic quantization equation and the energy
method. To prove the translational and rotational invariance of the
limit measure we take advantage of the fact that the symmetry groups of
the plane and the sphere have the same dimension. Joint work with Paweł
Duch and Wojciech Dybalski.