Ward-Type Identities for the Two-Dimensional Anderson Model at Weak Disorder

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Using the particular momentum conservation laws in dimension d = 2, we 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 the study of the weak-coupling model in the middle of the spectrum of the free Hamiltonian.

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