Gauge fields and Sternberg-Weinstein Approximation of Poisson Manifolds
| dc.creator | Maspfuhl, Oliver | |
| dc.date | 2004-03-30 | |
| dc.date.accessioned | 2026-07-07T04:31:03Z | |
| dc.date.available | 2026-07-07T04:31:03Z | |
| dc.description | The motion of a classical particle in a gravitational and a Yang-Mills field was described by S. Sternberg and A. Weinstein by a particular Hamiltonian system on a Poisson manifold known under the name of Sternberg-Weinstein phase space. This system leads to the generalization of the Lorentz equation of motion first discovered by Wong. The aim of this work is to show that inversely, a Hamiltonian H on a general Poisson manifold, with the property that its differential vanishes on a Lagrangian submanifold X of a symplectic leaf and is generic in any other direction, naturally defines a metric on X, as well as a principal connection form on a canonical principal fiber bundle on X. These fields, which are credited to model a gravitational and a Yang-Mills field on X, respectively, define a linearized Hamiltonian system of Wong type on a canonical linearized Poisson manifold at X locally isomorphic to a Sternberg-Weinstein phase space. In addition, H is shown to define scalar fields which first appeared in a theory of Einstein and Mayer. In the presence of a coisotropic constraint, the reduced system can be regarded as the phase space of particles in gravitational, Yang-Mills and Higgs fields. We further show that all our constructions are locally related to usual gauge and Kaluza-Klein theory via symplectic realization. | |
| dc.description | 48 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0403061 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0403061 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57686 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 53D17 | |
| dc.title | Gauge fields and Sternberg-Weinstein Approximation of Poisson Manifolds | |
| dc.type | text |