Cargando...
Fecha
2015-04-01
Derechos de acceso
info:eu-repo/semantics/openAccess
Título de la revista
ISSN de la revista
Título del volumen
Editorial
Elsevier
Citas
Resumen
In this work, we use the Sternberg phase space (which may be considered as the classical phase space of particles in gauge fields) in order to explore the dynamics of such particles in the context of Hamilton-Dirac systems and their associated Hamilton-Pontryagin variational principles. For this, we develop an analogue of the Pontryagin bundle in the case of the Sternberg phase space. Moreover, we show the link of this new bundle to the so-called magnetized Tulczyjew triple, which is an analogue of the link between the Pontryagin bundle and the usual Tulczyjew triple. Taking advantage of the
symplectic nature of the Sternberg space, we induce a Dirac structure on the Sternberg-Pontryagin bundle which leads to the Hamilton-Dirac structure that we are looking for. We also analyze the intrinsic and variational nature of the equations of motion of particles in gauge fields in regards of the defined new geometry. Lastly, we illustrate our theory through the case of a U(1) gauge group, leading to the paradigmatic example of an electrically charged particle in an electromagnetic field.
Descripción
The registered version of this article, first published in Journal of Geometry and Physics, is available online at the publisher's website:
Elsevier, https://doi.org/10.1016/j.geomphys.2015.03.011
La versión registrada de este artículo, publicado por primera vez en Journal of Geometry and Physics, está disponible en línea en el sitio web del editor: Elsevier, https://doi.org/10.1016/j.geomphys.2015.03.011
La versión registrada de este artículo, publicado por primera vez en Journal of Geometry and Physics, está disponible en línea en el sitio web del editor: Elsevier, https://doi.org/10.1016/j.geomphys.2015.03.011
Categorías UNESCO
Palabras clave
Hamilton–Dirac systems, Classical gauge fields, Tulczyjew triple, Dirac structures
Citación
Jiménez, F. (2015). Hamilton-Dirac systems for charged particles in gauge fields. Journal of Geometry and Physics, 94, 35-49. https://doi.org/10.1016/J.GEOMPHYS.2015.03.011
Centro
E.T.S. de Ingenieros Industriales
Departamento
Matemática Aplicada I