Vortrag
Euclidean field theories and interacting Bose gases
Vortrag von Prof. Dr. Antti Knowles
Datum: 23.11.23 Zeit: 16.15 - 18.00 Raum: ETH HG G 43
Euclidean field theories have been extensively studied in the mathematical literature since the sixties, motivated by high-energy physics and statistical mechanics. Formally, such a theory is given by a Gibbs measure associated with a Euclidean action functional over a space of distributions. In this talk I explain how some such theories arise as high-density limits of interacting Bose gases at positive temperature. This provides a rigorous derivation of them starting from a realistic microscopic model of statistical mechanics. I focus on field theories with a quartic, local or nonlocal, interaction in dimensions ≤ 3. Owing to the singularity of the Gaussian free field in dimensions higher than one, the interaction is ill-defined and has to be renormalized by infinite mass and energy counterterms. The proof is based on a new functional integral representation of the interacting Bose gas. Based on joint work with Jürg Fröhlich, Benjamin Schlein, and Vedran Sohinger.''