A new proposal for the fermion doubling problem. II. Improving the operators for finite lattices

TL;DR

This paper improves finite lattice operators for fermion derivatives by adjusting coefficients to eliminate truncation errors, enhancing accuracy without increasing computational cost.

Contribution

It introduces a method to correct finite lattice operators for fermion derivatives, reducing truncation errors through small coefficient adjustments.

Findings

Errors of order 1/N are effectively removed.

The correction method is computationally efficient.

The approach is pedagogically straightforward.

Abstract

In a previous paper I showed how the ideal SLAC derivative and second-derivative operators for an infinite lattice can be obtained in simple closed form in position space, and implemented very efficiently in a stochastic fashion for practical calculations on finite lattices. In this second paper I show how the small (order 1/N) errors introduced by truncating the operators to a finite lattice may be removed by a small adjustment of coefficients, without incurring any additional computational cost. The derivation of these results is again presented in a simple, pedagogical fashion.