  The f-sum rule is introduced and its applications to electronic and
vibrational modes are discussed. A related integral over the intra-band part of
sigma(omega) which is also valid for correlated electrons, becomes just the
kinetic energy if the only hopping os between nearest-neighbor sites. A summary
is given of additional sum-rule expressions for the optical conductivity and
the dielectric function, including expressions for the first and second moment
of the optical conductivity, and a relation between the Coulomb correlation
energy and the energy loss function. It is shown from various examples, that
the optical spectra of high Tc materials along the c-axis and in the ab-plane
direction can be used to study the kinetic energy change due to the appearance
of superconductivity. The results show, that the pairing mechanism is highly
unconventional, and mostly associated with a lowering of kinetic energy
parallel to the planes when pairs are formed. Keywords: Optical conductivity,
spectral weight, sum rules, reflectivity, dielectric function, inelastic
scattering, energy loss function, inelastic electron scattering, Josephson
plasmon, multi-layers, interlayer tunneling, transverse optical plasmon,
specific heat, pair-correlation, kinetic energy, correlation energy, internal
energy.
