  The isotropic scattering phase shift is calculated for non-relativistic
bosons interacting at low energies via an arbitrary finite-range potential in d
spacetime dimensions. Scattering on a (d-1)-dimensional torus is then
considered, and the eigenvalue equation relating the energy levels on the torus
to the scattering phase shift is derived. With this technology in hand, and
focusing on the case of two spatial dimensions, a perturbative expansion is
developed for the ground-state energy of N identical bosons which interact via
an arbitrary finite-range potential in a finite area. The leading non-universal
effects due to range corrections and three-body forces are included. It is then
shown that the thermodynamic limit of the ground-state energy in a finite area
can be taken in closed form to obtain the energy-per-particle in the
low-density expansion, by explicitly summing the parts of the finite-area
energy that diverge with powers of N. The leading and subleading finite-size
corrections to the thermodynamic limit equation-of-state are also computed.
Closed-form results --some well-known, others perhaps not-- for two-dimensional
lattice sums are included in an appendix.
