Restoring rotational invariance for lattice QCD propagators

This note presents a method to reduce the discretization errors appearing when solving a Quantum Field Theory in a hypercubic lattice in both position and momentum-space. The method exploits the artifacts that break rotational symmetry to recover rotationally invariant results for two-point Green functions. We show that a combination of the results obtained in position and momentum space can be useful to signal the presence of rotationally invariant artifacts making use of their approximate Fourier transforms in the continuum. The method will be introduced using a Klein-Gordon propagator, and a direct application to gluon propagator in quenched lattice QCD will be given.

Automated summary

This paper presents a method to reduce discretization errors in solving quantum field theory in a hypercubic lattice. The method utilizes artifacts that break rotational symmetry to obtain rotationally invariant results. By combining the results obtained in position and momentum space and using their approximate Fourier transforms in the continuum, the presence of rotationally invariant artifacts can be detected.