Many-body systems, interacting brownian motions, and functional integrals

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In this project we investigate the low-temperature behaviour of dilute quantum many-particle models. Our main interest is in understanding the dependence of the free energy density and correlation functions in the Gross-Pitaevskii limit, as well as generalisations of this limit which correspond to slightly larger densities. We consider both the canonical and the grand canonical ensemble. The former is studied via the interacting Brownian motion representation, using large deviations techniques, the latter via coherent-state functional integrals, using techniques from constructive quantum field theory. We also aim to investigate the connections between these two approaches.