Ground-State Energy of a Boson Gas

All the diagrams, occurring in a perturbation calculation of the ground-state energy of a boson gas, having at most one excited pair at a time, have been summed up using a variational principle, without explicitly writing their individual contributions. In the limit of large volumes the result of Abe is reproduced. It also turns out that the total contribution of all the diagrams is finite even though individually some of them are divergent irrespective of the strength of the interaction.