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Related papers: The overlap operator as a continued fraction

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We investigate the locality property of the overlap-Dirac operator on gauge configurations generated with extra Wilson fermions. By such extra terms we expect that the structure of the Aoki phase would change drastically. In particular, we…

High Energy Physics - Lattice · Physics 2012-11-09 Yong-Gwi Cho , Shoji Hashimoto

We first formulate an inverse problem for a linear fractional Lam\'e system. We determine the Lam\'e parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an…

Analysis of PDEs · Mathematics 2021-09-09 Li Li

We study the infrared part of the spectrum for UV-filtered staggered Dirac operators and compare them to the overlap counterpart. With sufficient filtering and at small enough lattice spacing the staggered spectra manage to ``mimic'' the…

High Energy Physics - Lattice · Physics 2009-11-10 Stephan Dürr , Christian Hoelbling , Urs Wenger

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…

Functional Analysis · Mathematics 2020-03-12 José Bonet

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 calculate the 2-loop partition function of QCD on the lattice, using the Wilson formulation for gluons and the overlap-Dirac operator for fermions. Direct by-products of our result are the 2-loop free energy and average plaquette. Our…

High Energy Physics - Lattice · Physics 2009-11-10 A. Athenodorou , H. Panagopoulos

We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of $n$-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the…

General Mathematics · Mathematics 2020-12-16 June-Haak Ee , Jungil Lee , Chaehyun Yu

The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a…

High Energy Physics - Lattice · Physics 2009-11-10 Luigi Del Debbio , Claudio Pica

A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in…

Nuclear Theory · Physics 2017-02-14 Z. X. Ren , S. Q. Zhang , J. Meng

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…

High Energy Physics - Lattice · Physics 2011-12-05 K. Splittorff , J. J. M. Verbaarschot

A transformation is devised to convert any lattice Dirac fermion operator into a Ginsparg-Wilson Dirac fermion operator. For the standard Wilson-Dirac lattice fermion operator, the transformed new operator is local, free of O(a) lattice…

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

I describe an implementation of the overlap action, which is built from an action which is itself an approximate overlap action. It appears to be about a factor of 15-20 less expensive to use, than the usual overlap action with the Wilson…

High Energy Physics - Lattice · Physics 2008-11-26 Thomas DeGrand

Using the grassman-number-integral representation of the vacuum overlap formula, it is shown that the symmetry of the auxiliary quantum fermion system in the overlap formalism induces exact chiral symmetry of the action of the type given by…

High Energy Physics - Lattice · Physics 2007-05-23 Yoshio Kikukawa , Atsushi Yamada

We study the eigenvalues of Dirac operators in QCD with two mass degenerate dynamical fermions. The gauge configurations have been obtained with HMC and the so-called Chirally Improved fermionic action. We compare eigenvalues obtained for…

High Energy Physics - Lattice · Physics 2009-04-14 Martina Joergler , C. B. Lang

We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps and compare them with algorithms based on lattice reduction.…

Number Theory · Mathematics 2023-03-15 Valerie Berthé , Karma Dajani , Charlene Kalle , Ela Krawczyk , Hamide Kuru , Andrea Thevis

The vacuum overlap formalism is extended to describe the supersymmetric multiplet of a Weyl fermion, a complex scalar boson and an auxiliary field in the case without interaction, based on the fact that supersymmetry can be maintained upto…

High Energy Physics - Lattice · Physics 2016-08-25 Tatsumi Aoyama , Yoshio Kikukawa

We measure the low lying eigenmodes of an overlap Dirac operator on 2--flavor staggered configurations. By comparing the eigenmode distribution to the predictions of Random Matrix Theory we test to what accuracy staggered configurations…

High Energy Physics - Lattice · Physics 2008-11-26 Anna Hasenfratz , Roland Hoffmann

Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\mathbb{R}^d$. We consider…

Dynamical Systems · Mathematics 2015-11-30 Sébastien Labbé

In the framework leading to the multiplicative anomaly formula ---which is here proven to be valid even in cases of known spectrum but non-compact manifold (very important in Physics)--- zeta-function regularisation techniques are shown to…

High Energy Physics - Theory · Physics 2009-10-31 Emilio Elizalde , Guido Cognola , Sergio Zerbini

We show that the spectral theory of the Dirac operator $D = i\delsl-\sigma(x) -i\pi(x)\gam_5$ in a static background $(\sigma(x),\pi(x))$ in 1+1 space-time dimensions, is underlined by a certain generalization of supersymmetric quantum…

High Energy Physics - Theory · Physics 2008-11-26 Joshua Feinberg