Noncommutative mechanics, Landau levels, Twistors, and Yang-Mills amplitudes

Abstract

These lectures fall into two distinct, although tenuously 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 the use of twistors in calculating Yang-Mills amplitudes. The point of connection between these two topics 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. © Springer 2006.