Editing Lattice QCD (section)

===Lattice perturbation theory===
In lattice perturbation theory physical quantities (such as the [[scattering matrix]]) are [[taylor expansion|expanded]] in powers of the lattice spacing, ''a''. The results are used primarily to [[renormalization|renormalize]] Lattice QCD Monte-Carlo calculations. In perturbative calculations both the operators of the action and the propagators are calculated on the lattice and expanded in powers of ''a''. When renormalizing a calculation, the coefficients of the expansion need to be matched with a common continuum scheme, such as the [[MS-bar scheme]], otherwise the results cannot be compared. The expansion has to be carried out to the same order in the continuum scheme and the lattice one.

The lattice regularization was initially introduced by [[Kenneth G. Wilson|Wilson]] as a framework for studying strongly coupled theories non-perturbatively. However, it was found to be a regularization suitable also for perturbative calculations. Perturbation theory involves an expansion in the coupling constant, and is well-justified in high-energy QCD where the coupling constant is small, while it fails completely when the coupling is large and higher order corrections are larger than lower orders in the perturbative series. In this region non-perturbative methods, such as Monte-Carlo sampling of the correlation function, are necessary.

Lattice perturbation theory can also provide results for [[condensed matter]] theory. One can use the lattice to represent the real atomic [[crystal]]. In this case the lattice spacing is a real physical value, and not an artifact of the calculation which has to be removed (a UV regulator), and a quantum field theory can be formulated and solved on the physical lattice.