Fermi Surface Approach to Inelastic Neutron Scattering Data in Cuprates*

A large body of calculations has been done to address inelastic neutron scattering data on cuprate superconductors based on linear response theory with a d-wave energy gap. I will review these calculations, emphasizing unique aspects that they can explain in regards to the data. This includes the magnetic resonance, with its unusual ``reversed magnon'' dispersion [1], and a novel new resonance mode which occurs at higher energies and at smaller momenta, which can account for the unusual ``45 degree rotation'' of the 2D momentum pattern seen in recent neutron data [2]. Finally, I will discuss limitations of these calculations in regards to certain experimental findings.\hfil\break [1] M. R. Norman, Phys. Rev. B 61, 14751 (2000) and 63, 092509 (2001).\hfil\break [2] I. Eremin, D. K. Morr, A. V. Chubukov, K. Bennemann, M. R. Norman, cond-mat/0409599