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 describ es two Dirac fields in the continuum limit, provided the coefficient l ambda of the Wilson-like term satisfies lambda > 1/2. In this letter i t is shown that for 1/2 < lambda less than or equal to 1 the theory is link-reflection positive. The propagator has the expected real energy poles. Module a phase shift on the fermions, the only relevant terms which can be added to the action respecting its symmetries have dimens ion 4.