Absence of species replication for a class of disordered fermion couplings

We present a disordered coupling scheme for free lattice fermions in two-dimensional spacetime. The theory is chirally invariant for a fermion mass of zero but does not lead to species replication and does not incorporate any long-range couplings. The fermion action breaks reflection positivity, the condition normally used to prove the existence of a self-adjoint hamiltonian for euclidean lattice field theories. Potential species replicas and states breaking reflection positivity decouple from processes which occur on a physical length scale because their wave functions become localized in the disordered lattice in somewhat the same way that electrons can become localized in a disordered solid. © 1986.