A diagrammatic two-particle locator theory for disordered systems. I. General formulation

A diagrammatic theory is established for the tight-binding model of independent electrons hopping in a disordered lattice as described by the Anderson Hamiltonian. The diagrammatic analysis starts from Anderson's locator expansion, gives a short review of the techniques already developed by several authors and finally arrives at a closed formulation of omega -dependent (R/A) particle-hole diagrams where retarded (R) and advanced (A) propagation differ by frequency omega and momentum q. Several different types of Bethe-Salpeter equations are considered and a new Ward identity valid for all omega , q is proved representing the key for the calculation of diffusional modes. It is shown that the formalism works equally well for weak and strong disorder.