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. doi:10.1016/0003-4916(86)90157-0. https://resolver.caltech.edu/CaltechAUTHORS:20100902-072124633
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Abstract
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.
| Item Type: | Article | ||||||
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| Additional Information: | © 1986 Academic Press, Inc. Received 8 January 1985. We are grateful to D. Bao. G. Gimmsy. D. Holm. A. Kaufman and T. Ratiu for helpful discussions and remarks. | ||||||
| Issue or Number: | 1 | ||||||
| DOI: | 10.1016/0003-4916(86)90157-0 | ||||||
| Record Number: | CaltechAUTHORS:20100902-072124633 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100902-072124633 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 19762 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Ruth Sustaita | ||||||
| Deposited On: | 09 Sep 2010 16:33 | ||||||
| Last Modified: | 08 Nov 2021 23:55 |
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