text: 2 
  v 
  4 
  6 
  7 
  0 
  . 
  1 
  0 
  0 
  1 
  : 
  v 
  i 
  X 
  r 
  a 
  
  ne2 
  m  π 
  2 
  Re σ(Ω) dΩ = 
  
  0 
  Z 
  
  Here n is the density of the electrons in the system and 
  m is the bare mass of the electron. This expression is 
  exact provided that the integration extends truly up to 
  inﬁnity, and its derivation uses the obvious fact that at 
  energies higher than the total bandwidth of a solid, elec- 
  trons behave as free particles. 
  
  The independence of the r.h.s. of Eq. (1) on temper- 
  ature and the state of a solid (e.g., a normal or a super- 
  conducting state – henceforth referred to as NS and SCS 
  respectively) implies that, while the functional form of 
  σ(Ω) changes with, e.g., temperature, the total spectral 
  weight is conserved and only gets redistributed between 
  diﬀerent frequencies as temperature changes. This con- 
  servation of the total weight of σ(Ω) is generally called a 
  sum rule. 