We computed the static potential and Wilson loops to O(α 2) in perturbation theory for different lattice quark and gluon actions. In general, we find short distance lattice data to be well described by " boosted perturbation theory ". For Wilson-type fermions at present-day quark masses and lattice spacings agreement within 10 % between measured " β-shifts " and those predicted by perturbation ...

We present a nonperturbative lattice formulation of noncommutative Yang-Mills theories in arbitrary even dimension. We show that lattice regularization of a noncommutative field theory requires finite lattice volume which automatically provides both an ultraviolet and an infrared cutoff. We demonstrate explicitly Morita equivalence of commutative U(p) gauge theory with p · nf flavours of fundam...

We study the heavy charge potential in the Coulomb phase of pure gauge compact U(1) theory on the lattice. We calculate the static potential VW (T, ~ R) from Wilson loops on a 16 × 32 lattice and compare with the predictions of lattice perturbation theory. We investigate finite size effects and, in particular, the importance of non–Coulomb contributions to the potential. We also comment on the ...

Based upon the mathematical formulas of Lattice gauge theory and non-commutative geometry differential calculus, we developed an approach of generalized gauge theory on a product of the spacetime lattice and the two discrete points(or a Z2 discrete group). We introduce a differentiation for non-nearest-neighbour points and find that this differentiation may lead to the introduction of Wilson te...

This article concerns a connection of fuzzy logic and lattice theory. Namely, the fuzzy sets form a Heyting lattice with union and intersection of fuzzy sets as meet and join operations. The lattice of fuzzy sets is defined as the product of interval posets. As the final result, we have characterized the composition of fuzzy relations in terms of lattice theory and proved its associativity.

We establish an asymptotic stability result for Toda lattice soliton solutions, by making use of a linearized Bäcklund transformation whose domain has codimension one. Combining a linear stability result with a general theory of nonlinear stability by Friesecke and Pego for solitary waves in lattice equations, we conclude that all solitons in the Toda lattice are asymptotically stable in an exp...