Atiyah, M. F. and Sutcliffe, P. M. (2002) 'The geometry of point particles.', Proceedings of the Royal Society A : mathematical, physical and engineering sciences., 458 (2021). pp. 1089-1115.
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.
|Keywords:||Point, Particles, Geometry, Energy, Minimization, Polyhedra.|
|Full text:||Full text not available from this repository.|
|Publisher Web site:||http://dx.doi.org/10.1098/rspa.2001.0913|
|Date accepted:||No date available|
|Date deposited:||No date available|
|Date of first online publication:||May 2002|
|Date first made open access:||No date available|
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