Perturbative analysis of the Neuberger-Dirac operator in the Schr\"odinger functional

Shinji Takeda

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Perturbative analysis of the Neuberger-Dirac operator in the Schr\"odinger functional

Shinji Takeda

High Energy Physics - Lattice · Submitted 10 Dec 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It turns out that the lattice artifacts for the Neuberger-Dirac operator are comparable in those of the clover action.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.42 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.90 · mentions code or data availability 0.02.

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We investigate the spectrum of the free Neuberger-Dirac operator $\Dov$ on the Schr\"odinger functional (SF). We check that the lowest few eigen-values of the Hermitian operator $\Dov^{\dag}\Dov$ in unit of $L^{-2}$ converge to the continuum limit properly. We also perform a one-loop calculation of the SF coupling, and then check the universality and investigate lattice artifacts of the step scaling function. It turns out that the lattice artifacts for the Neuberger-Dirac operator are comparable in those of the clover action.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the spectrum of the free Neuberger-Dirac operator $\Dov$ on the Schr\"odinger functional (SF).	contribution 1.00	0.94	0.04	asserted 0.79
s1	We check that the lowest few eigen-values of the Hermitian operator $\Dov^{\dag}\Dov$ in unit of $L^{-2}$ converge to the continuum limit properly.	result 0.75	0.93	0.07	asserted 0.95
s2	We also perform a one-loop calculation of the SF coupling, and then check the universality and investigate lattice artifacts of the step scaling function.	contribution 0.64	0.95	0.08	asserted 0.97
s3	It turns out that the lattice artifacts for the Neuberger-Dirac operator are comparable in those of the clover action.	result 0.98	0.89	0.57	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.72 · evidence from simulation or computation 0.56.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We investigate the spectrum of the free Neuberger-Dirac operator $\Dov$ on the Schr\"odinger functional (SF). We check that the lowest few eigen-values of the Hermitian operator $\Dov^{\dag}\Dov$ in unit of $L^{-2}$ converge to the continuum limit properly. We also perform a one-loop calculation of the SF coupling, and then check the universality and investigate lattice artifacts of the step scaling function. It turns out that the lattice artifacts for the Neuberger-Dirac operator are comparable in those of the clover action.

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3 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Compares with it 1 paper

We show numerical results for the one-loop deviation in Tables [ref] and [ref] and the plots in Figure [ref], where we include those of the Wilson type fermions [ref] and overlap fermion [ref] for comparison. $L_s$-dependence of DWFs is small.

A formulation of domain-wall fermions in the Schr\"odinger functional · Lattice artifacts of the step scaling function to one-loop order · 0.98

Cites it as background 1 paper

Some perturbative calculations were performed in Ref. [ref] .

A formulation of domain-wall fermions in the Schr\"odinger functional · Introduction · 0.80

What it cites · 35 sentences without a confident label

Uses the method or tool of 4 papers

From the Symanzik's analysis of the cutoff dependence of Feynman diagrams on the lattice, one expects that the one-loop coefficient has an asymptotic expansion [equation] We can reliably extract first several coefficients by making use of the method in Ref. [ref] .

Two Loop Computation of the Schroedinger Functional in Lattice QCD · Coefficients of Symanzik's expansion · 0.99
When one approximates the $X^-1/2$ by a polynomial of $X$ following Ref. [ref] , one needs information about the lower $u$ and upper $v$ bound of $X$.

Locality properties of Neuberger's lattice Dirac operator · Distribution of $ϵ$ · 0.92
Following Ref. [ref] , we implement the Remez algorithm to obtain minimax polynomials.

Numerical techniques for lattice QCD in the $\epsilon$--regime · How to build the Neuberger-Dirac operator · 1.00

Uses data or values from 2 papers

By combining the previous results from Ref. [ref] , the values of $A_0$ can be obtained, and are shown in the second line (numbers with $∗$) in each $s$ in Table [ref] for $θ=0,π/5$.

Lambda-parameter of lattice QCD with the overlap-Dirac operator · Coefficients of Symanzik's expansion · 0.92
By combining the previous results from Ref. [ref] , the values of $A_0$ can be obtained, and are shown in the second line (numbers with $∗$) in each $s$ in Table [ref] for $θ=0,π/5$.

The running coupling from the QCD Schr\"odinger functional -- a one-loop analysis · Coefficients of Symanzik's expansion · 0.92

Compares with 1 paper

We show numerical results of the one-loop deviation in Table [ref] and plots in Figure [ref], where we include those of the Wilson-Dirac and the clover action for comparison [ref] .

The running coupling from the QCD Schr\"odinger functional -- a one-loop analysis · Lattice artifacts of the step scaling function to one-loop order · 0.87

Cites as background 10 papers

Recently, formalisms for the Neuberger-Dirac operator on the SF have been proposed by Taniguchi [ref] and Lüscher [ref] .

The Schr\"odinger functional in lattice QCD with exact chiral symmetry · Introduction · 0.94
Recently, formalisms for the Neuberger-Dirac operator on the SF have been proposed by Taniguchi [ref] and Lüscher [ref] .

Schroedinger functional formalism with Ginsparg-Wilson fermion · Introduction · 0.94
A solution to a realization of the exact chiral symmetry on the lattice is proposed by Neuberger [ref] as the Neuberger-Dirac operator (overlap).

Exactly massless quarks on the lattice · Introduction · 0.91

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