A new approach to Ginsparg-Wilson fermions
Christof Gattringer (MIT)
TL;DR
This paper introduces a novel method for constructing Ginsparg-Wilson fermions by expanding the lattice Dirac operator in a basis, transforming the Ginsparg-Wilson equation into solvable quadratic equations for improved numerical solutions.
Contribution
It presents a new expansion technique for the lattice Dirac operator that enables precise numerical solutions to the Ginsparg-Wilson equation.
Findings
The method allows for arbitrary precision solutions.
The expansion provides a natural cutoff for the operator.
Quadratic equations are effectively solved numerically.
Abstract
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 to find Dirac operators which obey the Ginpsparg-Wilson equation with arbitrary precision.
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