On the chiral limit in lattice gauge theories with Wilson fermions

The chiral limit kappa similar or equal to kappa(c)(beta) in lattice gauge theories with Wilson fermions and problems related to near-to-zero ('exceptional') eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimator <(m)over tilde(pi)>, for the calculation of the pseudoscalar mass m(pi) is proposed which does not suffer from 'divergent' contributions at kappa similar or equal to kappa(c)(beta). We conclude that the main contribution to the pion mass comes from larger modes, and 'exceptional' eigenvalues play no physical role. The behaviour of the subtracted chiral condensate [<(psi)over bar psi>](subt) near kappa(c)(beta) is determined. We observe a comparatively large value of <(psi)over bar psi>(subt).Z(P)(-1), which could be interpreted as a possible effect of the quenched approximation.