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

Abstract

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.

44 pages, LaTeX, lectures at conferences

References in corpus (4)

• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes

Cited by in corpus (5)

• On the Landau system in noncommutative phase-space
• Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
• Massive Neutron Stars and White Dwarfs as Noncommutative Fuzzy Spheres