A Remnant of Chiral Symmetry on the Lattice

A new criterion for chiral symmetry in lattice theories of fermions is derived within a block-spin formalism. This ''remnant''-symmetry criterion properly incorporates the Adler-Bell-Jackiw anomaly and avoids the fermion-doubling problem of other lattice fermion methods. Some obstacles to implementing this approach in the presence of fully dynamical gauge fields are discussed.