Ward type identities for the 2d Anderson model at weak disorder
  Using the particular momentum conservation laws in dimension d=2, we can rewrite the Anderson model in terms of low momentum long range fields, at the price of introducing electron loops. The corresponding loops satisfy a Ward type identity, hence are much smaller than expected. This fact should be useful for a study of the weak-coupling model in the middle of the spectrum of the free Hamiltonian. 
Jacques Magnen, Gilles Poirot and Vincent Rivasseau (Ecole   Polytechnique, France)