Replica treatment of the Calogero–Sutherland model

Employing Forrester–Ha method of Jack polynomials, we derive an integral identity connecting certain N-fold coordinate average of the Calogero–Sutherland model with the n-fold replica integral. Subsequent analytical continuation in n leads to asymptotic expressions for the (static and dynamic) density–density correlation function of the model as well as the Green's function for an arbitrary coupling constant λ.