Planar Theory Made Variational

Within the framework of boson parquet-diagram summations in perturbation theory, we show analytically that several simple approximations lead inevitably to the radial distribution function $g\left(r\right)\mathrm{}$ which would be obtained with the Jastrow hypernetted-chain variational method. This is the first derivation of the Jastrow result from perturbation theory. Without mentioning pair-correlation functions, we have a clear interpretation of $g\left(r\right)\mathrm{}$ and the structure function, $S\left(k\right)\mathrm{}$, in terms of diagram sums.