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Related papers: Dirac operator normality and chiral properties

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The axial anomaly of Ginsparg-Wilson fermion operator $D$ is discussed in general for the operator $R$ which enters the chiral symmetry breaking part in the Ginsparg-Wilson relation. The axial anomaly and the index of $D$ as well as the…

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

All microscopic correlation functions of the spectrum of the Hermitian Wilson Dirac operator with any number of flavors with equal masses are computed. In particular, we give explicit results for the spectral density in the physical case…

High Energy Physics - Lattice · Physics 2013-05-29 K. Splittorff , J. J. M. Verbaarschot

Lower bounds on the magnitude of the spectrum of the Hermitian Wilson-Dirac operator H(m) have previously been derived for 0<m<2 when the lattice gauge field satisfies a certain smoothness condition. In this paper lower bounds are derived…

High Energy Physics - Lattice · Physics 2009-10-31 David H. Adams

Effects of dynamical quarks on the microscopic spectrum of the Wilson Dirac operator are analyzed by means of effective field theory. We consider the distributions of the real modes of the Wilson Dirac operator as well as the spectrum of…

High Energy Physics - Lattice · Physics 2011-07-15 G. Akemann , P. H. Damgaard , K. Splittorff , J. J. M. Verbaarschot

The fermionic determinant of a lattice Dirac operator that obeys the Ginsparg-Wilson relation factorizes into two factors that are complex conjugate of each other. Each factor is naturally associated with a single chiral fermion and can be…

High Energy Physics - Lattice · Physics 2008-11-26 Rajamani Narayanan

We derive the effective action of the light fermion field of the domain-wall fermion, which is referred as $q(x)$ by Furman and Shamir. The inverse of the effective Dirac operator turns out to be identical to the inverse of the truncated…

High Energy Physics - Lattice · Physics 2015-06-25 Y. Kikukawa , T. Noguchi

We summarize the analytical solution of the Chiral Perturbation Theory for the Hermitian Wilson Dirac operator of $N_c=2$ QCD with quarks in the fundamental representation. Results have been obtained for the quenched microscopic spectral…

High Energy Physics - Lattice · Physics 2015-05-20 Mario Kieburg , Jacobus Verbaarschot , Savvas Zafeiropoulos

We investigate a chiral property of the domain-wall fermion (DWF) system using the four-dimensional hermitian Wilson-Dirac operator $H_W$. A formula expressing the Ward-Takahashi identity quark mass $m_{5q}$ with eigenvalues of this…

We investigate chiral properties of the domain-wall fermion (DWF) system. After a brief introduction for the DWF, we summarize the recent numerical results on the chiral properties of the domain-wall QCD (DWQCD), which seem mutually…

High Energy Physics - Lattice · Physics 2009-11-07 Sinya Aoki

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations…

High Energy Physics - Lattice · Physics 2009-07-09 H. Neuberger

Some consequences which follow from the periodicity assumption for spectral density of Wilson--Dirac operator are studied. Such an assumption allows to obtain simple representations for quark propagator, which reveals an important role of…

High Energy Physics - Lattice · Physics 2007-05-23 Vladimir K. Petrov

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

Chiral properties of QCD formulated with the domain-wall fermion (DWQCD) are studied using the anomalous quark mass m_{5q} and the spectrum of the 4-dimensional Wilson-Dirac operator. Numerical simulations are made with the standard…

A chiral random matrix model with locality is constructed and examined. The Nielsen-Ninomiya no-go theorem is circumvented by the use of a generally applicable modified Dirac operator which respects the Ginsparg-Wilson relation. We observe…

High Energy Physics - Lattice · Physics 2007-05-23 K. Splittorff , A. D. Jackson

This article gives a review of the topic of regularising chiral gauge theories and is aimed at a general audience. It begins by clarifying the meaning of chirality and goes on to discussing chiral projections in field theory, parity…

High Energy Physics - Theory · Physics 2011-04-15 N. D. Hari Dass

We consider half-line Dirac operators with operator data of Wigner-von Neumann type. If the data is a finite linear combination of Wigner-von Neumann functions, we show absence of singular continuous spectrum and provide an explicit set…

Spectral Theory · Mathematics 2021-09-29 Ethan Gwaltney

According to the Banks-Casher formula the chiral order parameter is directly related to the spectrum of the Dirac operator. In this lecture, we will argue that some properties of the Dirac spectrum are universal and can be obtained from a…

High Energy Physics - Phenomenology · Physics 2007-05-23 J. J. M. Verbaarschot

We use the $\zeta$-function regularization and an integral representation of the complex power of a pseudo differential operator, to give an unambiguous definition of the determinant of the Dirac operator. We bring this definition to a…

High Energy Physics - Theory · Physics 2009-10-28 L. L. Salcedo , E. Ruiz Arriola

We present a method to solve the master equation for the Wilsonian action in the antifield formalism. This is based on a representation theory for cutoff dependent global symmetries along the Wilsonian renormalization group (RG) flow. For…

High Energy Physics - Theory · Physics 2009-11-07 Yuji Igarashi , Katsumi Itoh , Hiroto So

Only requiring that Dirac operators decribing massless fermions on the lattice decompose into Weyl operators we arrive at a large class of them. After deriving general relations from spectral representations we study correlation functions…

High Energy Physics - Lattice · Physics 2009-11-10 Werner Kerler