Dirac constraints in field theory: Lifts of Hamiltonian systems to the cotangent bundle

DOI10.1063/1.528175zbMath0656.70011OpenAlexW2038661951MaRDI QIDQ3804264

Walter Oevel

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.528175

zbMATH Keywords

cotangent bundleKorteweg-de Vries equationHamiltonian systemliftsDirac's theory of constraintsdegenerate Lagrangian formulation

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Classical field theories (70Sxx)

Related Items

On the maximum principle for ultraparabolic equations, Nonlinear integrable systems related to the elliptic Lie-Baxter algebra, The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy., Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems, On symmetry analysis of differential systems on functional manifolds, Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators, Integrable theory of the perturbation equations.

Cites Work

• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Hamiltonian operators and algebraic structures related to them
• The resolvent and Hamiltonian systems
• Korteweg-de Vries equation: a completely integrable Hamiltonian system
• Nonlinear stability of fluid and plasma equilibria
• Dirac’s theory of constraints in field theory and the canonical form of Hamiltonian differential operators
• Application of hereditary symmetries to nonlinear evolution equations
• Evolution equations possessing infinitely many symmetries