On attempts to avoid fermion doubling by giving up hermiticity

Abstract

Alessandrini and Krzywicki's (AK's) approximation to Weingarten and Velikson's (WV's) disordered coupling, non-hermitian fermion model is analysed and found to exhibit doubling. Thus the non-hermitian regular lattice model of Alonso and Cortes must also be discarded. We show that in the general non-hermitian regular lattice case there are extra zero modes and that in two dimensions the net chirality is zero. A better approximation of WV's model allows for the possibility of spontaneous chiral symmetry breaking of the doubled fermions in that model as in the random lattice case.