Euclidean Field Theories as Limit of Interacting Bose Gases

Explore the mathematical derivation of Euclidean field theories from interacting Bose gases in this 37-minute conference lecture. Learn how Euclidean field theories, extensively studied since the 1960s and motivated by high-energy physics and statistical mechanics, can be formally described by Gibbs measures associated with Euclidean action functionals over spaces of distributions. Discover recent developments showing how these theories emerge as high-density limits of interacting Bose gases at positive temperature, providing rigorous derivations from realistic microscopic models of statistical mechanics. Examine a recent result that derives such field theory with quartic local interaction in two dimensions as a limit of an inhomogeneous interacting Bose gas, extending previous work on the torus by Fröhlich-Knowles-Schlein-Sohinger. Gain insights into the mathematical physics perspective on quantum many-body systems and Bose-Einstein condensation through this research collaboration with Antti Knowles, Alessio Ranallo, and Pedro Torres Giesteira.