  We present an overview of the approach to establish a lower bound to the
ground state energy for the dilute, interacting Bose gas in a periodic box. In
this paper the size of the box is larger than the Gross-Pitaevski length scale.
The presentation includes both the 2 and 3 dimensional cases, and catches the
second order correction, i.e. the Lee-Huang-Yang term. The calculation on a box
of this length scale is the main step to calculate the energy in the
thermodynamic limit. However, the periodic boundary condition simplifies many
steps of the argument considerably compared to the localized problem coming
from the thermodynamic case.
