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 dimensions on a lattice with N sites. The
mapping to a U(N) one-plaquette model in the sense of Eguchi and Kawai can be used for
computer simulations. We are discussing the formulation and evaluation of topological objects.
We performed quantum Monte Carlo simulations and calculated the topological charge for
different matrix sizes and several values of the coupling constant. We constructed classical
gauge field configurations with large topological charge and used them to initialize quantum
simulations. It turned out that the value of the topological charge is decreasing during a Monte
Carlo history. Our results show that the topological charge is in general supressed. The situation
is similar to lattice QCD where quantum gauge field configurations are topologically trivial and
one needs to apply some cooling procedure on the gauge fields to unhide the integer number of
the instantons.
