Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-06-15
Lect.Notes Phys.698:97-138,2006
Physics
High Energy Physics
High Energy Physics - Theory
44 pages, LaTeX, lectures at conferences
Scientific paper
10.1007/3-540-33314-2_3
These lectures fall into two distinct, although tenouously related, parts. The first part is about fuzzy and noncommutative spaces, and particle mechanics on such spaces, in other words, noncommutative mechanics. The second part is a discussion/review of twistors and how they can be used in the calculation of Yang-Mills amplitudes. The point of connection between these two topics, discussed in the last section, is in the realization of holomorphic maps as the lowest Landau level wave functions, or as wave functions of the Hilbert space used for the fuzzy version of the two-sphere. This article is based on lectures presented at the conference on Higher Dimensional Quantum Hall Effect and Noncommutative Geometry, Trieste, March 2005, Winter School on Modern Trends in Supersymmetric Mechanics, Frascati, March 2005 and the Montreal-Rochester-Syracuse-Toronto Conference 2005, Utica, May 2005.
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