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Covariant Poisson Brackets for Classical Fields

Marsden, J. E. and Montgomery, R. and Morrison, P. J. and Thompson, W. B. (1986) Covariant Poisson Brackets for Classical Fields. Annals of Physics, 169 (1). pp. 29-47. ISSN 0003-4916.

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Poisson brackets that are spacetime covariant are presented for a variety of relativistic field theories. These theories include electromagnetism, general relativity, and general relativistic fluids and plasmas in Eulerian representation. The examples presented suggest the development of a general theory; the beginnings of such a theory are presented. Our covariant bracket formalism provides a general setting for, amongst other things, clarifying the transition from the covariant formalism to the dynamical 3 + 1 Hamiltonian formalism of Dirac and Arnowitt, Deser, and Misner. We illustrate the relevant procedures with electromagnetism.

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Additional Information:© 1986 Academic Press, Inc. Received 8 January 1985. Available online 29 September 2004. We are grateful to D. Bao. G. Gimmsy. D. Holm. A. Kaufman and T. Ratiu for helpful discussions and remarks.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19762
Deposited By: Ruth Sustaita
Deposited On:09 Sep 2010 16:33
Last Modified:26 Dec 2012 12:23

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