A contribution to the many-fermion problem

In this work we reexamine the many-fermion problem in arbitrary dimensions. It is shown that in two dimensions or higher, the Hamiltonian of interacting fermions can be separated into individual nonintersecting sectors labeled by the wave-vector q. Within each sector the Hamiltonian maps onto a generalized version of the one-dimensional Luttinger model that resembles a boson string. These are chain-like quadratic forms in boson operators that are readily diagonalized in the absence of "exchange" corrections. Moreover, in a simple example involving SU(2) fermions, that of the Hubbard model, we show that it can be possible also to incorporate exchange terms and express them entirely within an enlarged set of string variables.