Fermions

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 Euclidean dimensions, each fermionic field results in 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. (Wikipedia).

Fermion doubling
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Related pages

Nielsen–Ninomiya theorem | Group representation | Chiral anomaly | Translational symmetry | Quantum number | Lattice (group) | Action (physics) | Derivative | Dirac fermion | Hermitian matrix | Continuous function | Origin (mathematics) | Dirac algebra | Doublet state | Finite difference | Momentum | Dirac equation | Self-energy | Fermionic field | Periodic function | Spin (physics) | No-go theorem | Renormalization | Chirality (physics) | Brillouin zone | Principle of locality | Minkowski space | Maxima and minima | Gamma matrices | Fermion | Even and odd functions | Quadratic function | Modulo operation | Staggered fermion | Symmetry (physics) | Euclidean space | Energy | Zeros and poles | Contour integration | Eigenvalues and eigenvectors | Flavour (particle physics) | Correlation function (quantum field theory) | Fourier transform | Grassmann number