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arXiv · hep-th/9901112

Bering's proposal for boundary contribution to the Poisson bracket

Vladimir O. Soloviev
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Abstract

It is shown that the Poisson bracket with boundary terms recently proposed by Bering (hep-th/9806249) can be deduced from the Poisson bracket proposed by the present author (hep-th/9305133) if one omits terms free of Euler-Lagrange derivatives ("annihilation principle"). This corresponds to another definition of the formal product of distributions (or, saying it in other words, to another definition of the pairing between 1-forms and 1-vectors in the formal variational calculus). We extend the formula (initially suggested by Bering only for the ultralocal case with constant coefficients) onto the general non-ultralocal brackets with coefficients depending on fields and their spatial derivatives. The lack of invariance under changes of dependent variables (field redefinitions) seems a drawback of this proposal.

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Vladimir O. Soloviev. 1999-01-23. Bering's proposal for boundary contribution to the Poisson bracket. https://doi.org/10.1063/1.533414

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