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Related papers: A simple derivation of the Overlap Dirac Operator

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Three aspects of symmetry structure of lattice chiral fermion in the overlap formalism are discussed. By the weak coupling expansion of the overlap Dirac operator, the axial anomaly associated to the chiral transformation proposed by…

High Energy Physics - Lattice · Physics 2009-10-31 Y. Kikukawa

Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…

General Physics · Physics 2026-05-29 N. L. Chuprikov

I show how to avoid a two level nested conjugate gradient procedure in the context of Hybrid Monte Carlo with the overlap fermionic action. The resulting procedure is quite similar to Hybrid Monte Carlo with domain wall fermions, but is…

High Energy Physics - Lattice · Physics 2016-08-25 Herbert Neuberger

It is proved that the fermionic topological charge of SU(N) lattice gauge fields on the 4-torus, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of the Overlap Dirac operator, reduces…

High Energy Physics - Lattice · Physics 2015-06-25 David H. Adams

The coupling of spin 0 and spin 1 external fields to Dirac fermions defines a theory which displays gauge chiral symmetry. Quantum mechanically, functional integration of the fermions yields the determinant of the Dirac operator, known as…

High Energy Physics - Theory · Physics 2008-12-18 L. L. Salcedo

We describe the shape of the symplectic Dirac operators on Hermitian symmetric spaces. For this, we consider these operators as families of operators that can be handled more easily than the original ones.

Symplectic Geometry · Mathematics 2008-04-24 Steffen Brasch , Katharina Habermann , Lutz Habermann

In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a…

Representation Theory · Mathematics 2010-07-27 Vesa Tahtinen

We address the homogenization of the two-dimensional Dirac operator with position-dependent mass. The mass is piecewise constant and supported on small pairwise disjoint inclusions evenly distributed along an $\varepsilon$-periodic square…

Analysis of PDEs · Mathematics 2024-05-17 Andrii Khrabustovskyi , Vladimir Lotoreichik

On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides…

High Energy Physics - Theory · Physics 2009-11-11 Tamari T. Khachidze , Anzor A. Khelashvili

We compute the one-loop lattice renormalization of the two-quark operators $\bar{\psi} \Gamma \psi$, where $\Gamma$ denotes the generic Dirac matrix, for the lattice formulation of QCD using the overlap-Dirac operator. We also study the…

High Energy Physics - Lattice · Physics 2008-11-26 C. Alexandrou , E. Follana , H. Panagopoulos , E. Vicari

We launched a project to perform dymanical fermion simulations using the overlap fermion formulation for sea quarks. In order to avoid the appearace of near-zero modes of the hermitian Wilson-Dirac operator $H_W$, we introduce a pair of…

High Energy Physics - Lattice · Physics 2008-11-26 JLQCD collaboration , S. Hashimoto , S. Aoki , H. Fukaya , K. Kanaya , T. Kaneko , H. Matsufuru , M. Okamoto , T. Onogi , N. Yamada

We construct an explicit example of dimensional reduction of the free massless Dirac operator with an internal SU(3) symmetry, defined on a twelve-dimensional manifold that is the total space of a principal SU(3)-bundle over a…

High Energy Physics - Theory · Physics 2015-06-26 Petko A. Nikolov , Gergana R. Ruseva

We investigate a number of algorithms that calculate the quark propagators for the overlap-Dirac fermion operator. The QCD simulations were performed at beta = 5.9 with a lattice volume of 16**3*32.

High Energy Physics - Lattice · Physics 2015-06-25 UKQCD Collaboration , Craig McNeile , Alan Irving , Chris Michael

In this paper, we define a differential operator as a modified Dirac operator. Using the operator, we introduce a quaternionic $k$-vector field on a quaternionic K\"{a}hler manifold and show that any quaternionic $k$-vector field…

Differential Geometry · Mathematics 2021-09-16 Takayuki Moriyama , Takashi Nitta

We consider the three-dimensional Dirac operator coupled with a combination of electrostatic and Lorentz scalar $\delta$-shell interactions. We approximate this operator with general local interactions $V$. Without any hypotheses of…

Spectral Theory · Mathematics 2023-09-25 Mahdi Zreik

We present the universal one-loop effective action up to dimension eight after integrating out heavy fermion(s) using the Heat-Kernel method. We have discussed how the Dirac operator being a weak elliptic operator, the fermionic operator…

High Energy Physics - Phenomenology · Physics 2023-08-09 Joydeep Chakrabortty , Shakeel Ur Rahaman , Kaanapuli Ramkumar

We apply the technique of Hamiltonian reduction for the construction of three-dimensional ${\cal N}=4$ supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional ${\cal N}=4$…

High Energy Physics - Theory · Physics 2008-11-26 Stefano Bellucci , Armen Nersessian , Armen Yeranyan

We discuss the adaptation of the Hybrid Monte Carlo algorithm to overlap fermions. We derive a method which can be used to account for the delta function in the fermionic force caused by the differential of the sign function. We discuss the…

High Energy Physics - Lattice · Physics 2009-11-11 Nigel Cundy

We report on an ongoing project to parametrize the Fixed-Point Dirac operator for massless quarks, using a very general construction which has arbitrarily many fermion offsets and gauge paths, the complete Clifford algebra and satisfies all…

High Energy Physics - Lattice · Physics 2009-10-31 P. Hasenfratz , S. Hauswirth , K. Holland , T. Jorg , F. Niedermayer , U. Wenger

The concept of determinant for a linear operator in an infinite-dimensional space is addressed, by using the derivative of the operator's zeta-function (following Ray and Singer) and, eventually, through its zeta-function trace. A little…

High Energy Physics - Theory · Physics 2009-10-31 E. Elizalde