The Euclidean phi^4_2 theory as a limit of an interacting Bose gas
Antti Knowles (University of Geneva)
Abstract: Local Euclidean field theories over d-dimensional space have been extensively studied in the mathematical literature since the sixties, motivated by high-energy physics and statistical mechanics. For d=2, I explain how the complex scalar field theory with quartic interaction arises as a limit of an interacting Bose gas at positive temperature, when the density of the gas becomes large and the range of the interaction becomes small. The proof is based on a quantitative analysis of a new functional integral representation of the interacting Bose gas combined with a Nelson-type argument for a general nonlocal field theory. Joint work with Jürg Fröhlich, Benjamin Schlein, and Vedran Sohinger.
mathematical physics
Audience: researchers in the discipline
( video )
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