Speaker
Description
In this seminar we present the construction of equilibrium states at finite temperature for weakly interacting non-relativistic bosons with a non-trivial background field in infinitely extended space. Utilizing the framework introduced by Araki and further expanded by Fredenhagen and Lindner, we derive the generating function of the correlation functions of the theory as a suitable series. A Hubbard-Stratonovich transformation is then employed to reformulate this quantity. Estimates given in terms of the relative-entropy enable a rigorous analysis of the convergence of the associated loop vertex expansion within specific intermediate regimes. We isolate the tree diagrams that produce the scattering length in the dispersion relations of the two-point function of the state within the Gross-Pitaevskii regime. This scattering length is then used to renormalize both the background and the fluctuation two-point functions, concluding with a discussion about the bounds satisfied by the remainder.
Joint work with S. Galanda.