Castrillón López, Marco and Marsden, Jerrold E. (2003) Some remarks on Lagrangian and Poisson reduction for field theories. Journal of Geometry and Physics, 48 (1). pp. 52-83. ISSN 0393-0440. doi:10.1016/S0393-0440(03)00025-1. https://resolver.caltech.edu/CaltechAUTHORS:20100726-140606690
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Abstract
Given a Hamiltonian system on a fiber bundle, the Poisson covariant formulation of the Hamilton equations is described. When the fiber bundle is a G-principal bundle and the Hamiltonian density is G-invariant, the reduction of this formulation is studied thus obtaining the analog of the Lie-Poisson reduction for field theories. The relation of this reduction with the Lagrangian reduction and the Lagrangian and Poisson reduction for electromagnetism are also analyzed.
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| Additional Information: | © 2003 Elsevier. Received 17 December 2002; accepted 28 January 2003. Available online 2 April 2003. We thank Pedro Luis García, Jeffrey Lawson, Tudor Ratiu, Steve Shkoller and Jedrez Śniatycki for helpful remarks. The research of JEM was partially supported by NSF grant DMS-0204474 and a Max Planck research award, and MCL was partially supported by DGESIC (Spain) under grant no. BMF2000-1314 and Junta Castilla-Léon (Spain) under grant no. SA085-01. | |||||||||
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| Subject Keywords: | Lagrangian and Poisson reduction; Field theories | |||||||||
| Issue or Number: | 1 | |||||||||
| Classification Code: | MSC: 70S05 | |||||||||
| DOI: | 10.1016/S0393-0440(03)00025-1 | |||||||||
| Record Number: | CaltechAUTHORS:20100726-140606690 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100726-140606690 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 19184 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 27 Jul 2010 02:49 | |||||||||
| Last Modified: | 08 Nov 2021 23:50 |
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