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 http://resolver.caltech.edu/CaltechAUTHORS:20100902-072124633
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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.
|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.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||09 Sep 2010 16:33|
|Last Modified:||26 Dec 2012 12:23|
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