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Covariant and dynamical reduction for principal bundle field theories

Castrillón López, Marco and Marsden, Jerrold E. (2008) Covariant and dynamical reduction for principal bundle field theories. Annals of Global Analysis and Geometry, 34 (3). pp. 263-285. ISSN 0232-704X. doi:10.1007/s10455-008-9108-x.

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Reduction for field theories with symmetry can be done either covariantly—that is, on spacetime—or dynamically—that is, after spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle. One can think of this class of field theories as including examples such as a “sea of rigid bodies” with and appropriate interbody coupling potential.

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Additional Information:© Springer Science+Business Media B.V. 2008. Received: 10 August 2007 Accepted: 15 February 2008 Published online: 13 March 2008. We thank Tudor Ratiu and Mark Gotay for their helpful comments. The work of MCL was partially supported by Ministerio de Ecuación y Ciencia under grant MTM2007-60017. The work of JEM was partially supported by the National Science Foundation.
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Ministerio de Ecuación y CienciaMTM2007-60017
Subject Keywords:Variational calculus; Symmetries; Reduction; Euler–Poincare equations
Issue or Number:3
Record Number:CaltechAUTHORS:20100726-141918698
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19185
Deposited By: Ruth Sustaita
Deposited On:27 Jul 2010 23:23
Last Modified:08 Nov 2021 23:50

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