Some remarks on the Ginsparg-Wilson fermion

Abstract

We note that Fujikawa's proposal of generalization of the Ginsparg-Wilson relation is equivalent to setting $R=(a{\gamma }_{5}D{)}^{2k}$ in the original Ginsparg-Wilson relation $D{\gamma }_5+{\gamma }_{5}D=2aDR{\gamma }_{5}D$. An explicit realization of D follows from the Overlap construction. The general properties of D are derived. The chiral properties of these higher-order (k > 0) realizations of Overlap Dirac operator are compared to those of the Neuberger-Dirac operator (k = 0), in terms of the fermion propagator, the axial anomaly and the fermion determinant in a background gauge field. Our present results (up to lattice size 16 x 16) indicate that the chiral properties of the Neuberger-Dirac operator are better than those of higher-order ones.

20 pages, minor changes in v3, to appear in Nucl. Phys. B

References in corpus (1)

• Topological Phases in Neuberger-Dirac operator

Cited by in corpus (12)

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• The Index of a Ginsparg-Wilson Dirac operator
• Locality Properties of a New Class of Lattice Dirac Operators
• More chiral operators on the lattice
• Fermion determinant for general background gauge fields
• Domain wall fermion and CP symmetry breaking
• Ginsparg-Wilson relation with R=(a γ_5 D)^{2k}
• Can nonlocal Dirac operators be topologically proper ?
• A Perturbative Study of a General Class of Lattice Dirac Operators
• The Index and Axial Anomaly of a lattice Dirac operator