The Dirac theory of constraints, the Gotay-Nester theory and Poisson geometry

The Dirac theory of constraints has been widely studied and applied very successfully by physicists since the original works by Dirac and by Bergmann. From a mathematical standpoint, several aspects of the theory have been exposed rigorously afterwards by many authors. However, many questions relate...

Descripción completa

Detalles Bibliográficos
Autores principales: Cendra, Hernán, Etchechoury, María del Rosario, Ferraro, Sebastián José
Formato: Articulo
Lenguaje:Inglés
Publicado: 2012
Materias:
Matemática
Dirac´s theory of constraints
Poisson geometry
Presymlectic manifolds
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/101465
https://ri.conicet.gov.ar/11336/79889
https://www.ancefn.org.ar/contenido.asp?id=2302
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-101465
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Dirac´s theory of constraints
Poisson geometry
Presymlectic manifolds
spellingShingle Matemática
Dirac´s theory of constraints
Poisson geometry
Presymlectic manifolds
Cendra, Hernán
Etchechoury, María del Rosario
Ferraro, Sebastián José
The Dirac theory of constraints, the Gotay-Nester theory and Poisson geometry
topic_facet Matemática
Dirac´s theory of constraints
Poisson geometry
Presymlectic manifolds
description The Dirac theory of constraints has been widely studied and applied very successfully by physicists since the original works by Dirac and by Bergmann. From a mathematical standpoint, several aspects of the theory have been exposed rigorously afterwards by many authors. However, many questions related to, for instance, singular or infinite dimensional cases remain open. The work of Gotay and Nester presents a mathematical generalization in terms of presymplectic geometry, which introduces a dual point of view. We present a study of the Dirac theory of constraints emphasizing the duality between the Poisson-algebraic and the geometric points of view, related respectively to the work of Dirac and of Gotay and Nester, under strong regularity conditions. We deal with some questions insufficiently treated in the literature: a study of uniqueness of solution; avoiding almost completely the use of coordinates; the role of the Pontryagin bundle. We also show how one can globalize some results usually treated locally in the literature. For instance, we introduce the globalnotion of second class submanifoldas being tangent to a second class subbundle. A general study of global results for Dirac and Gotay-Nester theories remains an open question in this theory.
format Articulo
Articulo
author Cendra, Hernán
Etchechoury, María del Rosario
Ferraro, Sebastián José
author_facet Cendra, Hernán
Etchechoury, María del Rosario
Ferraro, Sebastián José
author_sort Cendra, Hernán
title The Dirac theory of constraints, the Gotay-Nester theory and Poisson geometry
title_short The Dirac theory of constraints, the Gotay-Nester theory and Poisson geometry
title_full The Dirac theory of constraints, the Gotay-Nester theory and Poisson geometry
title_fullStr The Dirac theory of constraints, the Gotay-Nester theory and Poisson geometry
title_full_unstemmed The Dirac theory of constraints, the Gotay-Nester theory and Poisson geometry
title_sort dirac theory of constraints, the gotay-nester theory and poisson geometry
publishDate 2012
url http://sedici.unlp.edu.ar/handle/10915/101465
https://ri.conicet.gov.ar/11336/79889
https://www.ancefn.org.ar/contenido.asp?id=2302
work_keys_str_mv AT cendrahernan thediractheoryofconstraintsthegotaynestertheoryandpoissongeometry
AT etchechourymariadelrosario thediractheoryofconstraintsthegotaynestertheoryandpoissongeometry
AT ferrarosebastianjose thediractheoryofconstraintsthegotaynestertheoryandpoissongeometry
AT cendrahernan diractheoryofconstraintsthegotaynestertheoryandpoissongeometry
AT etchechourymariadelrosario diractheoryofconstraintsthegotaynestertheoryandpoissongeometry
AT ferrarosebastianjose diractheoryofconstraintsthegotaynestertheoryandpoissongeometry
bdutipo_str Repositorios
_version_ 1764820442498990080

Ejemplares similares