The spin resonance and high frequency optical properties of the cuprates

We argue that recently observed superconductivity-induced blue shift of the plasma frequency $\delta \omega_{pl}$ in $Bi_2Sr_2CaCu_2O_{8+\delta}$ is related to the change in the integrated dynamical structure factor associated with the development of the spin resonance below $T_c$. We show that the magnitude of $\delta \omega_{pl}$ is consistent with the small integrated spectral weight of the resonance, and its temperature dependences closely follow that of the spin resonance peak.