Algebraic bosonisation: the case of the Dirac fermion

On the lattice fermions paired and then composed with precise phases are th e lattice bosons. We construct rules for deforming the underlying algebra t hat keep unchanged the boson interpretation. These deformations alter the p hases of the fermion pairs. The solutions of the deformed algebra are the p air-phase excitations of the lattice bosons. We find these eigenstates of t he Dirac Hamiltonian of fermions with mass. The gauge interactions are show n to excite the ie-deformed modes. (C) 2001 Published by Elsevier Science B .V.