A Note on Coadjoint Orbits for Multifermion Systems

Abstract

The coadjoint orbit action for a multifermion system, as an exact description of its dynamics, is considered. We also discuss two sequential approximations. The first involves a reduction to dynamics on the single-particle Hilbert space described by another coadjoint orbit action, suitable for expansions around the Fermi surface. A parametrization of the variables which facilitates this is given and we recover 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.