A Note on Coadjoint Orbits for Multifermion Systems

The coadjoint orbit action for a multifermion system, as an exact description of its dynamics, is considered. A parametrization of the variables involved is given which facilitates the approximation of this by another coadjoint orbit action suitable for expansions around the Fermi surface, recovering various actions which have been used in previous literature. The presentation of this in terms of functions on phase space with star-products as well as further truncations are briefly considered.