The Ground State Energy of a DiluteBose Gas yElliott

According to a formula that was put forward many decades ago the ground state energy per particle of an interacting, dilute Bose gas at density is 2~ 2 a=m to leading order in a 3 1, where a is the scattering length of the interaction potential and m the particle mass. This result, which is important for the theoretical description of current experiments on Bose-Einstein condensation, has recently been established rigorously for the rst time. We give here an account of the proof that applies to nonnegative, spherically symmetric potentials decreasing faster than 1=r 3 at innnity.