Factorization of Fermion Doubles on the Lattice

We address the problem of the fermion species doubling on the Lattice. Our strategy is to factorize the fermion doubles from the action. The mass term of the Dirac-Wilson action is changed. In this case the extra roots which appear in the action of free fermions in the moment representation are independent of the mass and can be factorized from the fermion propagator. However the gauge couplings suffer from the pathological ghost poles which are common to non-local actions. This action can be used to find a solution of the Ginsparg Wilson relation, which is cured from the non-local pathology. Finally we compare this factorized action with solutions of The Ginsparg Wilson relation. We find that the present is equivalent to the Zenkin action, and that is not quite as local as the Neuberger action.Comment: 7 Latex Revtex pages, 4 ps figures. The paper was improoved due to Comments received. It has a new section and several new reference

Spontaneous chiral symmetry breaking in the linked cluster expansion

We investigate dynamical chiral symmetry breaking in the Coulomb gauge Hamiltonian QCD. Within the framework of the linked cluster expansion we extend the BCS ansatz for the vacuum and include correlation beyond the quark-antiquark paring. In particular we study the effects of the three-body correlations involving quark-antiquark and transverse gluons. The high momentum behavior of the resulting gap equation is discussed and numerical computation of the chiral symmetry breaking is presented.Comment: 13 pages, 9 figure