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We derive exact equations for a broken scale invariance of the homogeneouselectron gas HEG, and show that they lead to a closed non-linear integralequation for the density- density correlation function when evaluated toleading order in the 1/N expansion. More generally, the identity leads to asequence of more refined systems of equations, which close on a finite numberof one plasmon irreducible (1PLI) correlation functions.

Broke Scale Invariance Ward Identities for the Homogeneous Electron Gas