A study of practical implementations of the overlap Dirac operator in four dimensions Original Research Article

We study three practical implementations of the overlap Dirac operator D̵0 = 12 [1+γϵ(Hw)] in four dimensions. Two implementations are based on different representations of ϵ(Hw) 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 ϵ(Hw) using Gegenbauer polynomials and is referred to as the fractional inverse method. After presenting some spectral properties of the Hermitian operator H0 = γ5D̵0, we study its spectrum in a smooth SU(2) instanton properties of the with the aim of comparing the three implementations of D0. We also present some results in SU(2) gauge field backgrounds generated at β = 2.5 on an 84 lattice. Chiral properties have been numerically verified.