Two-dimensional many-body problem I. the low-density hard-disk bose gas

The ground-state energy of a low-density hard-disk bose gas is analysed with a variational calculation. An upper bound, using a Jastrow trial function, and a lower bound are obtained which show the same leading functional dependence and hence the dependence of the lead term in the ground-state energy is firmly established. The upper-bound calculation is extended to provide estimates of succeeding terms. The calculation parallels calculations for the hard-sphere gas, but there is a marked difference in the treatment of the third term. Schick's results for the hard-disk gas are recovered. The upper bound for the leading term is generalized to pair potentials which do not support a two-body bound state and calculations for a two-dimensional Lennard-Jones fluid are discussed.