The conserving approximation scheme to many-body problems was developed by Kadanoff and Baym using the functional-derivative approach. Another approach for the Hubbard model also satisfies conservation laws, but in addition it satisfies the Pauli principle and a number of sum rules. A concise formal derivation of that approach, using functional derivatives, is given in this conference paper to highlight formal analogies and differences with conserving approximations.

1 aAllen, S1 aTremblay, A.-M., S.1 aVilk, Y M1 aSénéchal, D.1 aTremblay, A.-M., S.1 aBourbonnais, C uhttps://www.physique.usherbrooke.ca/pages/en/node/7226