Efficient numerical techniques for perturbative lattice gauge theory computations

Abstract

We discuss a set of methods and numerical tools, which are useful for a computer based approach to perturbative calculations in lattice gauge theory. The topics considered include the automatic generation of gluon vertex programs, a derivation of the Faddeev-Popov determinant on lattices with boundary, the use of a partially finite lattice with twisted boundary conditions as an infrared cutoff without zero modes, and finally the numerical extrapolation of lattice Feynman diagrams to the continuum limit. As an illustration of the methods we describe their implementation in the computation of the on-shell improved lattice action at weak coupling.