Freiburg 2008 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 7: Nichtkommutative Geometrie

MP 7.3: Talk

Thursday, March 6, 2008, 14:40–15:00, KGI-HS 1023

Recent Results on the Topology of Non-commutative Geometry on the Lattice — Wolfgang Frisch¹, Harald Grosse², •Harald Markum¹, and Florian Teischinger¹ — ¹Atominstitut, Vienna University of Technology, Austria — ²Department for Theoretical Physics, University of Vienna, Austria

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 [1]. The mapping to a U(N) one-plaquette model in the sense of Eguchi and Kawai can be used for computer simulations. We are interested in the formulation and evaluation of topological objects [2]. 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. Our recent analyses will be presented [3].
W. Bietenholz et al., Fortsch. Phys. 53 (2005) 418
H. Aoki, J. Nishimura, Y. Susaki, hep-th/0602078
W. Frisch, H. Grosse, H. Markum, PoS(LAT2007)317