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

Abstract

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 $\lambda =1/2,1,and2$, and conjecture that a similar relation may hold for arbitrary rational $\lambda$.

4 pages, REVTeX+multicol.sty, to be published in Phys. Rev. E

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