Lattice fermion discretisation
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
formula_1
is introduced supplementing the naively discretized Dirac action in formula_2-dimensional Euclidean spacetime with lattice spacing formula_3, Dirac fields formula_4 at every lattice point formula_5, and the vectors formula_6 being unit vectors in the formula_7 direction. The inverse free fermion propagator in momentum space now reads
formula_8
where the last addend corresponds to the Wilson term again. It modifies the mass formula_9 of the doublers to
formula_10
where formula_11 is the number of momentum components with formula_12. In the continuum limit
formula_13 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 formula_14.
References.
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