On the spherical symmetry and finite-range assumptions of the interaction potential in the low energy study of dilute Bose gases

We consider a Bose gas on the three-dimensional torus in the Gross–Pitaevskii regime and explain how to remove the assumptions of radiality and compact support on the interaction potential in the proof of Bose–Einstein condensation and convergence of the excitation spectrum to Bogoliubov’s prediction. In particular, we sketch the proof of [50].