München 2009 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantentheorie großer Systeme

MP 3.3: Vortrag

Dienstag, 10. März 2009, 14:40–15:00, M010

Instantons in Noncommutative U(1) Gauge Theory in Even Dimensions on the Lattice — Arifa Ali Khan¹ and •Harald Markum² — ¹Institute of Theoretical Physics, University of Regensburg — ²Atominstitut, Vienna University of Technology

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 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. At present we are working out the definition of instantons and monopoles in 4 dimensions. Concerning the topological charge it seems straightforward. and one can transcribe the plaquette and hypercube formulation to the matrix theory. The monopole observable seems to be more difficult. The analogy to commutative U(1) theory of summing up the phases of an elementary cube might need a projection on the abelian part of the U(N) theory in the matrix model.