Nielsen–Ninomiya theorem
No-go theorem concerning chirality of regularized fermions / From Wikipedia, the free encyclopedia
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In lattice field theory, the Nielsen–Ninomiya theorem is a no-go theorem about placing chiral fermions on a lattice. In particular, under very general assumptions such as locality, hermiticity, and translational symmetry, any lattice formulation of chiral fermions necessarily leads to fermion doubling, where there are the same number of left-handed and right-handed fermions. It was first proved by Holger Bech Nielsen and Masao Ninomiya in 1981 using two methods, one that relied on homotopy theory[1] and another that relied on differential topology.[2] Another proof provided by Daniel Friedan uses differential geometry.[3] The theorem was also generalized to any regularization scheme of chiral theories.[4] One consequence of the theorem is that the Standard Model cannot be put on a lattice.[5] Common methods for overcoming the fermion doubling problem is to use modified fermion formulations such as staggered fermions, Wilson fermions, or Ginsparg–Wilson fermions, among others.