Chiral invariance and lattice fermions with minimal doubling

A few years ago some attention has been given to a fermionic action on the lattice, with a Wilson-like term which is chirally invariant but breaks the hypercubic space-time lattice symmetry. This action describes two Dirac fields in the continuum limit, provided the coefficient λ of the Wilson-like term satisfies λ > 12. In this letter it is shown that for 12 < λ ≤ 1 the theory is link-reflection positive. The propagator has the expected real energy poles. Modulo a phase shift on the fermions, the only relevant terms which can be added to the action respecting its symmetries have dimension 4.