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Some remarks on Lagrangian and Poisson reduction for field theories

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.

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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.
Funding AgencyGrant Number
DGESIC (Spain)BMF2000-1314
Junta Castilla-Léon (Spain)SA085-01
Subject Keywords:Lagrangian and Poisson reduction; Field theories
Issue or Number:1
Classification Code:MSC: 70S05
Record Number:CaltechAUTHORS:20100726-140606690
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19184
Deposited By: Ruth Sustaita
Deposited On:27 Jul 2010 02:49
Last Modified:08 Nov 2021 23:50

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