Atiyah, Michael and Sutcliffe, Paul M.
(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 .
(doi:10.1098/rspa.2001.0913)
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Official URL http://rspa.royalsocietypublishing.org/content/458... |

## Abstract

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.

Item Type: | Article |
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Additional information: | Full-text freely avilable via Official URL link. |

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: | 16 Jun 2014 09:28 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/7968 (The current URI for this page, for reference purposes) |

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