Abstract
We prove the following formula for the ground state energy density of a dilute Bose gas with density ρ in 2 dimensions in the thermodynamic limit [Formula: see text] as ρa2 → 0 . Here Y = |log(ρa2)|-1 and a is the scattering length of the two-body potential. This result in 2 dimensions corresponds to the famous Lee-Huang-Yang formula in 3 dimensions. The proof is valid for essentially all positive potentials with finite scattering length, in particular, it covers the crucial case of the hard core potential.