English
Related papers

Related papers: Improving the Dirac Operator in Lattice QCD

200 papers

The Overlap-Dirac operator provides a lattice regularization of massless vector gauge theories with an exact chiral symmetry. Practical implementations of this operator and recent results in quenched QCD using this Overlap-Dirac operator…

High Energy Physics - Lattice · Physics 2007-05-23 Robert G. Edwards , Urs M. Heller , Rajamani Narayanan

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…

High Energy Physics - Lattice · Physics 2011-02-16 Ting-Wai Chiu

The condition for a lattice Dirac operator D to reproduce correct chiral anomaly at each site of a finite lattice for smooth background gauge fields is that D possesses exact zero modes satisfying the Atiyah-Singer index theorem. This is…

High Energy Physics - Lattice · Physics 2015-06-25 Ting-Wai Chiu

A new class of lattice Dirac operators which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands…

High Energy Physics - Lattice · Physics 2009-10-31 Kazuo Fujikawa , Masato Ishibashi

We discuss some properties of zero and near-zero modes of the Dirac operator, as observed in a recent simulation of 2-flavor QCD. The quarks have been implemented with the so-called Chirally Improved Dirac operator, which obeys the…

High Energy Physics - Lattice · Physics 2007-05-23 C. B. Lang , Pushan Majumdar , Wolfgang Ortner

Measurements of the lowest-lying eigenvalues of the staggered fermion Dirac operator are made on ensembles of equilibrium gauge field configurations in quenched SU(3) lattice gauge theory. The results are compared with exact analytical…

High Energy Physics - Lattice · Physics 2009-10-31 P. H. Damgaard , U. M. Heller , A. Krasnitz

A perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} =…

High Energy Physics - Lattice · Physics 2016-09-01 Kazuo Fujikawa , Masato Ishibashi

Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form…

High Energy Physics - Lattice · Physics 2016-09-01 Kazuo Fujikawa

The gauge covariant lattice Dirac operator D which has recently been proposed by Neuberger satisfies the Ginsparg-Wilson relation and thus preserves chiral symmetry. The operator also avoids a doubling of fermion species, but its locality…

High Energy Physics - Lattice · Physics 2011-07-19 P. Hernández , K. Jansen , M. Lüscher

In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral lagrangian (including weak interaction couplings) by performing numerical simulations in the $\epsilon$--regime, i.e. at quark masses where the…

High Energy Physics - Lattice · Physics 2011-07-19 L. Giusti , C. Hoelbling , M. Lüscher , H. Wittig

We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the…

High Energy Physics - Lattice · Physics 2013-11-20 H. Fukaya , S. Aoki , G. Cossu , S. Hashimoto , T. Kaneko , J. Noaki

We apply the topology conserving gauge action proposed by Luescher to the four-dimensional lattice QCD simulation in the quenched approximation. With this gauge action the topological charge is stabilized along the hybrid Monte Carlo…

High Energy Physics - Lattice · Physics 2009-11-11 H. Fukaya , S. Hashimoto , T. Hirohashi , K. Ogawa , T. Onogi

The overlap operator is a lattice discretization of the Dirac operator of quantum chromodynamics, the fundamental physical theory of the strong interaction between the quarks. As opposed to other discretizations it preserves the important…

High Energy Physics - Lattice · Physics 2014-10-28 James Brannick , Andreas Frommer , Karsten Kahl , Björn Leder , Matthias Rottmann , Artur Strebel

We study some interesting aspects of the spectral properties of SU(3) gauge theory, both with and without dynamical quarks (QCD) at thermal equilibrium using lattice gauge theory techniques. By calculating the eigenstates of a massless…

High Energy Physics - Lattice · Physics 2026-03-05 Harshit Pandey , Ravi Shanker , Sayantan Sharma

We provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing $K$-theory to classify the Wilson Dirac operator via its spectral flow. In contrast to the index of the overlap Dirac operator defined…

High Energy Physics - Lattice · Physics 2026-02-27 Shoto Aoki , Hajime Fujita , Hidenori Fukaya , Mikio Furuta , Shinichiroh Matsuo , Tetsuya Onogi , Satoshi Yamaguchi

We argue that lattice QCD with Ginsparg-Wilson fermions satisfies the Leutwyler-Smilga sum rules for the eigenvalues of the chiral Dirac operator. The result is obtained in the one flavor case, by rephrasing Leutwyler and Smilga's original…

High Energy Physics - Lattice · Physics 2007-05-23 F. Farchioni

I describe a mechanism to understand the relation between chiral-symmetry breaking and eigenmodes of the Dirac operator in lattice QCD with Kogut-Susskind sea quarks. It can be shown that if chiral symmetry is spontaneously broken, the…

High Energy Physics - Lattice · Physics 2009-10-31 Xiang-Qian Luo

We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action…

High Energy Physics - Lattice · Physics 2009-10-31 F. Farchioni , I. Hip , C. B. Lang , M. Wohlgenannt

It was recently proposed by the second author to consider lattice formulations of QCD in which complete actions, including the gauge part, are built explicitly from a given Dirac operator D. In a simple example of such theory, the gauge…

High Energy Physics - Lattice · Physics 2008-11-26 Andrei Alexandru , Ivan Horvath , Keh-Fei Liu

We compare the behavior of different lattice Dirac operators in gauge backgrounds which are lattice discretizations of a classical instanton. In particular we analyze the standard Wilson operator, a chirally improved Dirac operator and the…

High Energy Physics - Lattice · Physics 2008-11-26 Christof Gattringer , Meinulf Göckeler , C. B. Lang , P. E. L. Rakow , Andreas Schäfer