Ground state energy of the low density bose gas

Now that the properties of low temperature Bose gases at low density, ρ, can be examined exprimentally it is appropriate to revisit some of the formulas deduced by many authors four to five decades ago. One of these is that the leading term in the energy/particle is 2π Latin small letter h with stroke² ρa/m, where a is the scattering length. Owing to the delicate and peculiar nature of bosonic correlations, four decades of research have failed to establish this plausible formula rigorously. The only known lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct bound is proved here.