Optical sum in nearly antiferromagnetic Fermi liquid model

We calculate the optical sum (OS) and the kinetic energy (KE) for a tight binding band in the nearly antiferromagnetic Fermi liquid model which has had some success in describing the electronic structure of the high-T-c cuprates. The interactions among electrons due to the exchange of spin fluctuations profoundly change the probability of occupation (n(k,sigma)) of states of momentum k and spin sigma 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.