Publication details for Paul SutcliffeAtiyah, M.F. & Sutcliffe, P.M. (2002). The Geometry of Point Particles. Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences 458(2021): 1089-1115.
- Publication type: Journal Article
- ISSN/ISBN: 1364-5021, 1471-2946
- DOI: 10.1098/rspa.2001.0913
- Keywords: Point Particles Geometry Energy Minimization Polyhedra
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
There is a very natural map from the configuration space of n distinct points in Euclidean 3-space into the flag manifold U(n)/U(1)n, which is compatible with the action of the symmetric group. The map is well defined for all configurations of points provided a certain conjecture holds, for which we provide numerical evidence. We propose some additional conjectures, which imply the first, and test these numerically. Motivated by the above map, we define a geometrical multi-particle energy function and compute the energy-minimizing configurations for up to 32 particles. These configurations comprise the vertices of polyhedral structures that are dual to those found in a number of complicated physical theories, such as Skyrmions and fullerenes. Comparisons with 2- and 3-particle energy functions are made. The planar restriction and the generalization to hyperbolic 3-space are also investigated.