2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/205362The overlap operator is just the simplest of a class of Dirac operators with an exact chiral symmetry. I demonstrate how a general class of chiral Dirac operators can be constructed, show that they have no fermion doublers and that they are all exponentially local, and test my conclusions numerically for a few examples. However, since these operators are more expensive than the overlap operator, it is unlikely that they will be useful in practical simulations.14 pages, 3 figures; v2 typos corrected, references and small additional section added; v3 major changes to the introduction and concluding sections; some typos corrected; to appear in Nucl. Phys. BHigh Energy Physics - Latticetext