Fermion doubling

In lattice field theory, fermion doubling occurs when naively putting fermionic fields on a lattice, resulting in more fermionic states than expected. For the naively discretized Dirac fermions in ${\displaystyle d}$ Euclidean dimensions, each fermionic field results in ${\displaystyle 2^{d}}$ identical fermion species, referred to as different tastes of the fermion. The fermion doubling problem is intractably linked to chiral invariance by the Nielsen–Ninomiya theorem. Most strategies used to solve the problem require using modified fermions which reduce to the Dirac fermion only in the continuum limit.