Dirac’s theory of constraints in field theory and the canonical form of Hamiltonian differential operators

DOI10.1063/1.527315zbMath0609.70010OpenAlexW1984529541MaRDI QIDQ3750172

Peter J. Olver

Publication date: 1986

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527315

zbMATH Keywords

infinite-dimensional systemsDarboux problemfinite-dimensional Hamiltonian systemscanonical coordinatesHamiltonian functionalDirac's theory of constraintsdegenerate Lagrangianskew-adjoint Hamiltonian differential operatorskew-symmetric symplectic matrix

Mathematics Subject Classification ID

Hamilton's equations (70H05) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items (7)

Classification results and the Darboux theorem for low-order Hamiltonian operators ⋮ Darboux' theorem for Hamiltonian differential operators ⋮ On Hamiltonian formulations of the \(\mathcal{C}_1(m, a, b)\) equations ⋮ Canonical structures for dispersive waves in shallow water ⋮ Dirac constraints in field theory: Lifts of Hamiltonian systems to the cotangent bundle ⋮ Canonical Hamiltonian representation of the Krichever--Novikov equation ⋮ Compactons

Cites Work

• Hamiltonian operators and algebraic structures related to them
• Mathematics of dispersive water waves
• Symplectic manifolds and their Lagrangian submanifolds
• Nonlinear stability of fluid and plasma equilibria
• Generalized Hamiltonian dynamics
• Canonical formulation of shallow water waves
• Hamiltonian perturbation theory in noncanonical coordinates
• Hamiltonian perturbation theory and water waves
• On the Hamiltonian structure of evolution equations
• A resolution of the Euler operator II
• A simple model of the integrable Hamiltonian equation
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
• Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System

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