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In the continuum the definitions of the covariant Dirac operator and of the gauge covariant derivative operator are tightly intertwined. We point out that the naive discretization of the gauge covariant derivative operator is related to the existence of local unitary operators which allow the definition of a natural lattice gauge covariant derivative. The associated lattice Dirac operator has all the properties of the classical continuum Dirac operator, in particular antihermiticy and chiral invariance in the massless limit, but is of course non-local in accordance to the Nielsen-Ninomiya theorem. We show that this lattice Dirac operator coincides in the limit of an infinite lattice volume with the naive gauge covariant generalization of the SLAC derivative, but contains non-trivial boundary terms for finite-size lattices. Its numerical complexity compares pretty well on finite lattices with smeared lattice Dirac operators.
Topological objects of $SU(3)$ gluodynamics are studied at the infrared scale near the transition temperature with the help of zero and near-zero modes of the overlap Dirac operator. We construct UV filtered topological charge densities corresponding to thr
We discuss the weak coupling expansion of lattice QCD with the overlap Dirac operator. The Feynman rules for lattice QCD with the overlap Dirac operator are derived and the quark self-energy and vacuum polarization are studied at the one-loop level.
We investigate the Operator Product Expansion (OPE) on the lattice by directly measuring the product <Jmu Jnu> (where J is the vector current) and comparing it with the expectation values of bilinear operators. This will determine the Wilson coeffici
Starting from the chiral Lagrangian for Wilson fermions at nonzero lattice spacing we have obtained compact expressions for all spectral correlation functions of the Hermitian Wilson Dirac operator in the $epsilon$-domain of QCD with dynamical quarks
We compute the overlap Dirac spectrum on three ensembles generated using 2+1 flavor domain wall fermions. The spectral density is determined up to $lambdasim$100 MeV with sub-percentage statistical uncertainty. The three ensembles have different latt