The local Gauss law of quantum chromodynamics on a finite lattice is investigated. It is shown that it implies a gauge invariant, additive law giving rise to a gauge invariant Z3-valued global charge in QCD. The total charge contained in a region of the lattice is equal to the flux through its boundary of a certain Z3-valued, additive quantity. Implications for continuous QCD are discussed.

Hopf solitons in the Skyrme-Faddeev model — S 2-valued fields on R 3 with Skyrme dynamics — are string-like topological solitons. In this Letter, we investigate the analogous lattice objects, for S 2-valued fields on the cubic lattice Z 3 with a nearest-neighbour interaction. For suitable choices of the interaction, topological solitons exist on the lattice. Their appearance is remarkably simil...

We prove that an n-valued function that is lower semi-continuous is also upper semi-continuous and therefore continuous, that is, an n-valued map. Several conditions are shown to be equivalent to continuity for n-valued functions, in particular the continuity of a corresponding singlevalued function to a configuration space. Consequently, splitting is related to braid groups to prove a Splittin...

Recently, I. Stubbe constructed an isomorphism between the categories of right Q-modules and cocomplete skeletal Q-categories for a given unital quantale Q. Employing his results, we obtain an isomorphism between the categories of Q-algebras and Q-quantales, where Q is additionally assumed to be commutative. As a consequence, we provide a common framework for two concepts of lattice-valued fram...

Morphing composite structures are of significant interest due to the fact that they exhibit superior mass-to-stiffness ratios and a large degree tailorability in comparison traditional materials structures. One such morphing structure is multistable cylindrical lattice. Current work introduces novel variable-topology mechanism it through use both permanent magnets electromagnets. By replacing s...

The overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, realizes exact chiral symmetry on the lattice. It also avoids fermion doubling but its locality and smoothness are subtle. In fact, the index theorem on the lattice implies that there are certain points where the overlap Dirac operator has discontinuities. Aside from the theoretical subtleties, this non-smoothness also ra...