text: The issue of sum rule attracted substantial interest in 
  the studies of high Tc cuprates5–18,21–26 in which pairing 
  is without doubts a strong coupling phenomenon. From a 
  theoretical perspective, the interest in this issue was orig- 
  inally triggered by a similarity between WK and the ki- 
  ε~kn~k.18–20 For a model with a sim- 
  netic energy K = 2 
  ple tight binding cosine dispersion εk ∝ (cos kx + cos ky), 
  d2 ε~k 
  ∼ −ε~k and WK = −K. For a more complex dis- 
  d k2 
  x 
  persion there is no exact relation between WK and K, 
  but several groups argued 17,27,28 that WK can still be 
  regarded as a good monitor for the changes in the kinetic 
  energy. Now, in a BCS superconductor, kinetic energy 
  increases below Tc because nk extends to higher frequen- 
  cies (see Fig.2). At strong coupling, K not necessary 
  increases because of opposite trend associated with the 
  fermions are more mobile in the 
  fermionic self-energy: 
  SCS due to less space for scattering at low energies than 
  they are in the NS. Model calculations show that above 
  some coupling strength, the kinetic energy decreases be- 
  29. While, as we said, there is no one-to-one cor- 
  low Tc 
  respondence between K and WK, it is still likely that, 
  when K decreases, WK increases. 
  
  P 