Boundary values as Hamiltonian variables. I. New Poisson brackets

Abstract

The ordinary Poisson brackets in field theory do not fulfil the Jacobi identity if boundary values are not reasonably fixed by special boundary conditions. We show that these brackets can be modified by adding some surface terms to lift this restriction. The new brackets generalize a canonical bracket considered by Lewis, Marsden, Montgomery and Ratiu for the free boundary problem in hydrodynamics. Our definition of Poisson brackets permits to treat boundary values of a field on equal footing with its internal values and directly estimate the brackets between both surface and volume integrals. This construction is applied to any local form of Poisson brackets. A prescription for delta-function on closed domains and a definition of the {\it full} variational derivative are proposed.

26 pages, LaTex, IHEP 93-48

Cited by in corpus (30)

• The Constraint Algebra of Topologically Massive AdS Gravity
• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Effective Conformal Descriptions of Black Hole Entropy
• Poisson brackets in Hydrodynamics
• Energy and the AdS/CFT Correspondence
• Consistent boundary conditions for supergravity
• Putting an Edge to the Poisson Bracket
• Black hole entropy from Poisson brackets (demystification of some calculations)
• Dirac's algorithm in the presence of boundaries: a practical guide to a geometric approach
• Boundary conditions from boundary terms, Noether charges and the trace K lagrangian in general relativity
• Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. I. General Consideration
• Family of Boundary Poisson Brackets
• Physics-to-gauge conversion at black hole horizons
• Canonical Structure of Field Theories with Boundaries and Applications to Gauge Theories
• The spinning particle with curved target
• Bering's proposal for boundary contribution to the Poisson bracket
• Nonlinear two-dimensional water waves with arbitrary vorticity
• On the Difference between Admissible and "Differentiable" Hamiltonians
• Symplectic approach to lightcone QCD
• A Darboux-Getzler theorem for scalar difference Hamiltonian operators
• Boundary terms and their Hamiltonian dynamics
• Canonical analysis of field theories in the presence of boundaries: Maxwell+Pontryagin
• Free Boundary Poisson Bracket Algebra in Ashtekar's Formalism
• Weakly Isolated Horizons: $3+1$ decomposition and canonical formulations in self-dual variables
• Intrinsic Time in Geometrodynamics of Closed Manifolds
• Black Hole Statistical Physics: Entropy
• A note on the Hamiltonian structure of transgression forms
• Batalin-Vilkovisky formality for Chern-Simons theory
• Product of Boundary Distributions
• The partition function versus boundary conditions and confinement in the Yang-Mills theory