Optical sum in Nearly Antiferromagnetic Fermi Liquid Model

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We calculate the optical sum (OS) and the kinetic energy (KE) for a tight binding band in the Nearly Antiferromagnetic Fermi Liquid (NAFFL) model which has had some success in describing the electronic structure of the high Tc cuprates. The interactions among electrons due to the exchange of spin fluctuations profoundly change the probability of occupation (n k,σ) of states of momentum k and spin σ which is the central quantity in the calculations of OS and KE. Normal and superconducting states are considered as a function of temperature. Both integrals are found to depend importantly on interactions and an independent electron model is inadequate.