Normal modes of the d>1 fermion gas

In the present work we solve the many-fermion problem in dimensions greater than one by identifying its normal modes. We start by decomposing the Fermi sea into independent sectors labeled by a wavevector q. The product of exactly calculable eigenstates, one from each sector, is an exact eigenstate of the full many-body problem. We examine bosonization of fermions, exchange and pairing forces and quasiparticles, all from this point of view.