Bering's proposal for boundary contribution to the Poisson bracket

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.

18 pages, LaTeX, amssymb

References in corpus (4)

• Symmetry Algebras in Chern-Simons Theories with Boundary: Canonical Approach
• Boundary values as Hamiltonian variables. I. New Poisson brackets
• Boundary terms and their Hamiltonian dynamics
• Divergences as a grading of the formal variational calculus

Cited by in corpus (5)

• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Dirac's algorithm in the presence of boundaries: a practical guide to a geometric approach
• Canonical analysis of field theories in the presence of boundaries: Maxwell+Pontryagin
• Weakly Isolated Horizons: $3+1$ decomposition and canonical formulations in self-dual variables
• A note on the Hamiltonian structure of transgression forms