as the diluteness parameter $\rho a^3 \rightarrow 0$. Here $a$ is the scattering length of the interaction potential. This is the celebrated Lee-Huang-Yang formula for the energy density.
Understanding the energy to this precision requires a detailed understanding of correlations between the particles. Therefore, and because of the link between such energy questions and the property of Bose-Einstein Condensation of dilute gases of bosonic particles, proving such formulas for the energy density has been an area of intense activity in the mathematical physics community in recent years. This effort has also lead to a rigorous understanding of the Bogoliubov approximation for the interacting Bose gas.
In this talk, I will in particular review parts of the proof (joint with Jan Philip Solovej) of the Lee-Huang-Yang formula for the energy. I will also comment on the harder 2-dimensional case and how the proof can be modified to accommodate this case.
