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Journal of Mathematical Physics / Volume 29 / Issue 1

J. Math. Phys. 29, 210 (1988); http://dx.doi.org/10.1063/1.528175 (10 pages)

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

Walter Oevel

Universitaet Paderborn, D4790 Paderborn, Federal Republic of Germany

(Received 11 June 1987; accepted 26 August 1987)

To every Hamiltonian system is associated a degenerate Lagrangian formulation. Following Dirac’s theory of constraints one finds a family of lifts of the system to the cotangent bundle of the underlying manifold. The lifted system admits a reduction to the original equation such that the original Hamiltonian formulation is the pullback of the canonical symplectic form. Invariants of the original equation can be lifted to invariants of the extended system. This procedure is applied to integrable systems such as the Korteweg–de Vries equation.

KEYWORDS and PACS

Keywords

FIELD THEORIES, NONLINEAR PROBLEMS, HAMILTONIANS, QUANTUM FIELD THEORY, KORTEWEG−DE VRIES EQUATION, CANONICAL TRANSFORMATIONS, DYNAMICAL SYSTEMS, INTEGRABLE SYSTEMS, FIBER BUNDLES

PACS

  • 11.10.Ef

    Lagrangian and Hamiltonian approach

  • 11.10.Lm

    Nonlinear or nonlocal theories and models

  • 11.30.Na

    Nonlinear and dynamical symmetries (spectrum-generating symmetries)

  • 45.05.+x

    General theory of classical mechanics of discrete systems

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.528175

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    P. J. Olver, “Dirac's theory of constraints in field theory and the canonical form of Hamiltonian differential operators,” J. Math. Phys. 27, 2495 (1986JMAPAQ000027000010002495000001).

    P. J. Olver, “Evolution equations possessing infinitely many symmetries,” J. Math. Phys. 18, 1212 (1977JMAPAQ000018000006001212000001).



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