A review of lattice fermion formulations, centered on a non-Hermitian one-sided-difference approach that avoids doublers while preserving chiral symmetry, plus surveys of Wilson, overlap, topological charge, and Monte Carlo methods.
The Index of a Ginsparg-Wilson Dirac operator
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abstract
A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configurations.
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Lattice Chiral Fermion without Hermiticity
A review of lattice fermion formulations, centered on a non-Hermitian one-sided-difference approach that avoids doublers while preserving chiral symmetry, plus surveys of Wilson, overlap, topological charge, and Monte Carlo methods.