Atiyah, M. and Sutcliffe, P. (2002) The geometry of point particles. Proceedings of the Royal Society A- Mathematical Physical and Engineering Sciences, 458 (2021). pp. 1089-1115. ISSN 1364-5021 .
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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.
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|Uncontrolled keywords:||point particles; geometry; energy minimization; polyhedra EQUILIBRIUM-CONFIGURATIONS; CHARGES; SPHERE|
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics|
|Depositing User:||Judith Broom|
|Date Deposited:||14 Sep 2008 13:06|
|Last Modified:||14 Jan 2010 14:29|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/7968 (The current URI for this page, for reference purposes)|
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