Application of the linked cluster expansion to the many-particle path-integral

A diagrammatic expansion for the pair distribution can be derived by starting from the many-body path-integral and using the idea of cluster expansion. The expansion is written as a sum of nodal and non-nodal diagrams. The sum of all the nodal diagrams can be expressed in terms of the non-nodal diagrams using the hypernetted equation technique. The sum of the non-nodal diagrams, which are irreducible diagrams in momentum space, are written as a perturbation expansion in powers of the particle density. Our approach is analogous to the well-known many-body perturbation expansion of the n-body Green's function. The approach was tested on a system of distinguishable particles and our results agree very well with those obtained from the path-integral Monte Carlo.