出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：Theories with noncommutative space-time coordinates represent alternative candidates of grand unified theories. We discuss U(1) gauge theory in 2 and 4 dimensions on a lattice with N sites. The mapping to a U(N) plaquette model in the sense of Eguchi and Kawai can be used for computer simulations. In 2D it turns out that the formulation of the topological charge leads to the imaginary part of the plaquette. Concerning 4D, the definition of instantons seems straightforward. We show that one can transcribe the plaquette and hypercube formulation to the matrix theory. It will be interesting to measure the topological charge on a noncommutative hypercube.
