Reduction of polysymplectic manifolds
The aim of this paper is to generalize the classical Marsden-Weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which inherit the polysymplectic structure. This generalization allows us to reduce polysymplectic Hamiltonian systems...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/77056 |
| Acceso en línea: | https://hdl.handle.net/2117/77056 https://dx.doi.org/10.1088/1751-8113/48/5/055206 |
| Access Level: | acceso abierto |
| Palabra clave: | Hamiltonian systems polysymplectic manifolds Marsden-Weinstein reduction k-coadjoint orbits polysymplectic Hamiltonian systems NONHOLONOMIC MECHANICAL SYSTEMS CLASSICAL FIELD-THEORY MULTI-MOMENT MAPS SYMMETRIES FORMALISM DYNAMICS SPACES Hamilton, Sistemes de Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| Sumario: | The aim of this paper is to generalize the classical Marsden-Weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which inherit the polysymplectic structure. This generalization allows us to reduce polysymplectic Hamiltonian systems with symmetries, such as those appearing in certain kinds of classical field theories. As an application of this technique, an analogue to the Kirillov-Kostant- Souriau theorem for polysymplectic manifolds is obtained and some other mathematical examples are also analyzed. Our procedure corrects some mistakes and inaccuracies in previous papers (Gunther 1987 J. Differ. Geom. 25 23-53; Munteanu et al 2004 J. Math. Phys. 45 1730-51) on this subject. |
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