Appears in collection : Dam Thanh Son : Bosonization of Fermi Surface : The Method of Coadjoint Orbits

Fermi liquid theory is a cornerstone of condensed matter physics. However, Landau's Fermi liquid theory does not fit into the paradigm of effective field theory in that it is formulated in terms of a kinetic equation rather than an action. We describe a new method that leads to a field-theoretical reformulation of Landau Fermi liquid theory. In this approach, a system with a Fermi surface is described as a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonization of the Fermi surface. The Berry phase that the Fermi surface acquires when changing shape is shown to be given bythe Kirillov-Kostant-Souriau symplectic form on the coadjoint orbit. We show that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. Possible extensions and applications of the theory are described.