Abstract
In the theory of integrable systems and in other field theories one usually deals with Poisson brackets between functionals. The latter are integrals of densities. Densities are defined up to divergence (boundary) terms. A question arises, is it possible to define a reasonable Poisson bracket for densities themselves? A general theory was suggested by Barnich, Fulp, Lada, Markl and Stasheff which has led them to the notion of a strong homotopy Lie group, (sh Lie). We are giving a few concrete examples.
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References
Barnich, G., Fulp, R., Lada, T., and Stasheff, J. (1997): The sh Lie structure of Poisson brackets in field theory. To be published
Olver, P.J. (1993): Applications of Lie groups to differential equations. 2nd ed., Springer
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© 1998 Springer-Verlag
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Dickey, L.A. (1998). Poisson brackets for densities of functionals. In: Aratyn, H., Imbo, T.D., Keung, WY., Sukhatme, U. (eds) Supersymmetry and Integrable Models. Lecture Notes in Physics, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105313
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DOI: https://doi.org/10.1007/BFb0105313
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