In lattice field theory, the Ginsparg–Wilson equation generalizes chiral symmetry on the lattice in a way that approaches the continuum formulation in the continuum limit.
They are a means to avoid the fermion doubling problem, widely used for instance in lattice QCD calculations.
[1] The equation was discovered by Paul Ginsparg and Kenneth Wilson in 1982,[2] however it was quickly forgotten about since there were no known solutions.
Ginsparg–Wilson fermions do not contradict the Nielsen–Ninomiya theorem because they explicitly violate chiral symmetry.
is the massless Dirac operator) is replaced by the Ginsparg–Wilson equation[6][7][8] which recovers the correct continuum expression as the lattice spacing
The exact form of this modification depends on the individual realisation.