Parametric Ward-Takahashi identity in disordered systems and the integral identity associated with the Calogero-Sutherland model

By utilizing the symmetric property known as the Ward-Takahashi identity in disordered systems, we explore the novel symmetry relations which hold in one-dimensional systems with inverse square interaction (the Calogero-Sutherland model). The identities emerge totally from the algebraic structure of the model. They show that the dynamical correlators are connected with one another, involving the higher-order integrals of motion. We obtain the result for the coupling strengths $\lambda=1/2, 1, and 2$, and conjecture that a similar relation may hold for arbitrary rational $\lambda$.