Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1998-07-08
Nucl.Phys.B540:457-471,1999
Physics
High Energy Physics
High Energy Physics - Lattice
23 pages latex with 9 postscript figures included by epsf. Some change in referencing and one figure modified
Scientific paper
10.1016/S0550-3213(98)00694-4
We study three practical implementations of the Overlap-Dirac operator $D_o= (1/2) [1 + \gamma_5\epsilon(H_w)]$ in four dimensions. Two implementations are based on different representations of $\epsilon(H_w)$ as a sum over poles. One of them is a polar decomposition and the other is an optimal fit to a ratio of polynomials. The third one is obtained by representing $\epsilon(H_w)$ using Gegenbauer polynomials and is referred to as the fractional inverse method. After presenting some spectral properties of the Hermitian operator $H_o=\gamma_5 D_o$, we study its spectrum in a smooth SU(2) instanton background with the aim of comparing the three implementations of $D_o$. We also present some results in SU(2) gauge field backgrounds generated at $\beta=2.5$ on an $8^4$ lattice. Chiral properties have been numerically verified.
Edwards Robert G.
Heller Urs M.
Narayanan Rajamani
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