Wilson fermion
In lattice field theory, Wilson fermions are a fermion discretization that allows to avoid the fermion doubling problem proposed by Kenneth Wilson in 1974. They are widely used, for instance in lattice QCD calculations. An additional so-called Wilson term

is introduced supplementing the naively discretized Dirac action in -dimensional Euclidean spacetime with lattice spacing , Dirac fields  at every lattice point , and the vectors  being unit vectors in the  direction. The inverse free fermion propagator in momentum space now reads

where the last addend corresponds to the Wilson term again. It modifies the mass  of the doublers to

where  is the number of momentum components with . In the continuum limit
 the doublers become very heavy and decouple from the theory. Wilson fermions do not contradict the Nielsen–Ninomiya theorem because they explicitly violate chiral symmetry since the Wilson term does not anti-commute with . References 

Lattice field theory
Fermions