Group theoretic and graphical techniques are used to derive the N-body wavefunction for a system of identical bosons with general interactions throughfirst-order in a perturbation approach. This method is based on the maximalsymmetry present at lowest order in a perturbation series in inverse spatialdimensions. The symmetric structure at lowest order has a point groupisomorphic with the S_N group, the symmetric group of N particles, and theresulting perturbation expansion of the Hamiltonian is order-by-order invariantunder the permutations of the S_N group. This invariance under S_N imposessevere symmetry requirements on the tensor blocks needed at each order in theperturbation series. We show here that these blocks can be decomposed into abasis of binary tensors invariant under S_N. This basis is small (25 terms atfirst order in the wave function), independent of N, and is derived usinggraphical techniques. This checks the N^6 scaling of these terms at first orderby effectively separating the N scaling problem away from the rest of thephysics. The transformation of each binary tensor to the final normalcoordinate basis requires the derivation of Clebsch-Gordon coefficients of S_Nfor arbitrary N. This has been accomplished using the group theory of thesymmetric group. This achievement results in an analytic solution for the wavefunction, exact through first order, that scales as N^0, effectivelycircumventing intensive numerical work. This solution can be systematicallyimproved with further analytic work by going to yet higher orders in theperturbation series.
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