We expand the most general lattice Dirac operator D in a basis of simple operators. The Ginsparg-Wilson equation turns into a system of coupled quadratic equations for the expansion coefficients. Our expansion of D allows for a natural cutoff and the remaining quadratic equations can be solved numerically. The procedure allows us to find Dirac operators which obey the Ginpsparg-Wilson equation with arbitrary precision.
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Christof Gattringer (2001) studied this question.
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