A geometric study of many body systems
| dc.creator | Straume, Eldar | |
| dc.date | 2006-09-05 | |
| dc.date.accessioned | 2026-07-07T07:24:19Z | |
| dc.date.available | 2026-07-07T07:24:19Z | |
| dc.description | A n n-body system is a labelled collection of n point masses in Euclidean space, and their congruence and internal symmetry properties involve a rich mathematical structure which is investigated in the framework of equivariant Riemannian geometry. Some basic concepts are n-configuration, configuration space, internal space, shape space, Jacobi transformations and weighted root system. The latter is a generalization of the root system of SU(n), which provides a bookkeeping for expressing the mutual distances of the point masses in terms of the Jacobi vectors. Moreover, its application to the study of collinear central n-configurations yields a simple proof of Moulton's enumeration formula. A major topic is the general study of matrix spaces representing the shape space of many body systems in Euclidean k-space, the structure of the m-universal shape space and its O(m)-equivariant linear model.This also leads to those orbital fibrations where SO(m) or O(m) act on a sphere with a sphere as orbit space. Some examples of this kind are encountered in the literature, e.g. the special case of the 5-sphere mod O(2), which equals the 4-sphere, was analyzed independently by Arnold, Kuiper and Massey in the 1970's. | |
| dc.description | 58 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0609008 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0609008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116303 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Geometric Topology | |
| dc.subject | 70F10,70G40, 57R99 | |
| dc.title | A geometric study of many body systems | |
| dc.type | text |