Ground state energy of the interacting Bose gas in two dimensions: an explicit construction

Understand

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.