Non-Abelian finite-element gauge theory Original Research Article

We complete the formulation of the equations of motion of a non-Abelian gauge field coupled to fermions on a finite-element lattice in four space-time dimensions. This is accomplished by a straightforward iterative approach, in which successive interaction terms are added to the Dirac and Yang-Mills equations of motion, and to the field strength, in order to preserve lattice gauge invariance exactly, yielding a series in powers of ghA. Here g is the coupling constant, h is the lattice spacing, and A is the gauge potential. Gauge transformations of the potentials are determined simultaneously. The interaction terms in the equations of motion are non-local, and an be expressed either by an iterative formula or by a difference equation. On the other hand, the field strength is locally constructed from the potentials in terms of a path-ordered product of exponentials.