Abstract
It is shown that the Poisson bracket with boundary terms proposed by Bering can be deduced from the Poisson bracket proposed by the present author 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 for the ultralocal case with constant coefficients only) onto the general nonultralocal brackets with coefficients depending on fields and their spatial derivatives. The lack of invariance under changes of dependent variables (field redefinitions) seems to be a drawback of this proposal.
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