Overlap Operator

The overlap operator is a lattice Dirac operator introduced by Herbert Neuberger that realizes exact chiral symmetry on the lattice through a non-local projection of the Wilson-Dirac operator. It satisfies the Ginsparg-Wilson relation, a lattice analogue of the continuum chiral algebra, and provides the formal foundation for domain-wall fermions, which approximate it in a local five-dimensional formulation. The operator is computationally expensive but mathematically pristine, making it the gold standard for chiral lattice QCD.