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Covariant and Dynamical Reduction for Principal Bundle Field Theories

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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

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Official URL: http://link.springer.com/content/pdf/10.1007%2Fs10455-008-9108-x.pdf


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Variational calculus · Symmetries · Reduction · Euler–Poincare equations
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:22027
Deposited On:20 Jun 2013 14:55
Last Modified:12 Dec 2018 15:13

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