Inequivalence of the zero-momentum Limits of Transverse and Longitudinal Dielectric Response in the Cuprates

In this talk, I will address the question of the mismatch between the zero momentum limits of the transverse (optical conductivity) and longitudinal (momentum resolved EELS) dielectric functions observed in the cuprates. This question translates to whether or not the order in which the longitudinal and transverse momentum transfers are taken to zero commute. While the two limits commute for both isotropic and anisotropic Drude metals, I will argue that a scaleless vertex interaction is sufficient to achieve non-commutativity of the two limits even for a system that is inherently isotropic.