We have developed a new method for bosonizing the Fermi surface based on the formalism of the coadjoint orbits. This allows one to parametrize the Fermi surface by a bosonic field that depends on the spacetime coordinates and on the position on the Fermi surface. The Wess–Zumino–Witten term in the effective action, governing the adiabatic phase acquired when the Fermi surface changes its shape, is given by the Kirillov–Kostant–Souriau symplectic form on the coadjoint orbit. Together with a Hamiltonian, the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. Extensions of the theory that incorporate spin degrees of freedom and the BCS order parameter are discussed.
Host: Yuan Xin (yuan.xin@yale.edu)