Lattice Gauge Theory - Basics

Basics

In lattice gauge theory, the spacetime is Wick rotated into Euclidean space and discretized into a lattice with sites separated by distance and connected by links. In the most commonly considered cases, such as lattice QCD, fermion fields are defined at lattice sites (which leads to fermion doubling), while the gauge fields are defined on the links. That is, an element U of the compact Lie group G is assigned to each link. Hence to simulate QCD, with Lie group SU(3), there is a 3×3 special unitary matrix defined on each link. The link is assigned an orientation, with the inverse element corresponding to the same link with the opposite orientation.