%0 Generic %1 frohlich2020pathintegral %A Fröhlich, Jürg %A Knowles, Antti %A Schlein, Benjamin %A Sohinger, Vedran %D 2020 %K field mean theory %T A path-integral analysis of interacting Bose gases and loop gases %U http://arxiv.org/abs/2001.11714 %X We review some recent results on interacting Bose gases in thermal equilibrium. In particular, we study the convergence of the grand-canonical equilibrium states of such gases to their mean-field limits, which are given by the Gibbs measures of classical field theories with quartic Hartree-type self-interaction, and to the Gibbs states of classical gases of point particles. We discuss various open problems and conjectures concerning, e.g., Bose-Einstein condensation, polymers and $\phi \vert^4$-theory.

@misc{frohlich2020pathintegral, abstract = {We review some recent results on interacting Bose gases in thermal equilibrium. In particular, we study the convergence of the grand-canonical equilibrium states of such gases to their mean-field limits, which are given by the Gibbs measures of classical field theories with quartic Hartree-type self-interaction, and to the Gibbs states of classical gases of point particles. We discuss various open problems and conjectures concerning, e.g., Bose-Einstein condensation, polymers and $\vert \boldsymbol{\phi} \vert^{4}$-theory.}, added-at = {2020-02-03T19:30:02.000+0100}, author = {Fröhlich, Jürg and Knowles, Antti and Schlein, Benjamin and Sohinger, Vedran}, biburl = {https://www.bibsonomy.org/bibtex/292187c4f1793924218d0f784775fea49/gzhou}, description = {A path-integral analysis of interacting Bose gases and loop gases}, interhash = {4021b02c598801b6267f54eb18bf625d}, intrahash = {92187c4f1793924218d0f784775fea49}, keywords = {field mean theory}, note = {cite arxiv:2001.11714Comment: 21 pages, no figures, contribution to special volume of J. Stat. Phys. dedicated to Joel L. Lebowitz}, timestamp = {2020-02-03T19:30:02.000+0100}, title = {A path-integral analysis of interacting Bose gases and loop gases}, url = {http://arxiv.org/abs/2001.11714}, year = 2020 }