Invariant variational problems on principal bundles and conservation laws

Ján Brajerčík

Displaying similar documents to “Invariant variational problems on principal bundles and conservation laws”

${Gl}_{n} (R)$ -invariant variational principles on frame bundles.

Brajerčik, J. (2008)

Balkan Journal of Geometry and its Applications (BJGA)

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A new Lagrangian dynamic reduction in field theory

François Gay-Balmaz, Tudor S. Ratiu (2010)

Annales de l’institut Fourier

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For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group...

Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles

Ján Brajerčík (2011)

Czechoslovak Mathematical Journal

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Let $μ : F X \to X$ be a principal bundle of frames with the structure group ${Gl}_{n} (ℝ)$ . It is shown that the variational problem, defined by ${Gl}_{n} (ℝ)$ -invariant Lagrangian on $J^{r} F X$ , can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.

Equivariance, variational principles, and the Feynman integral.

Svetlichny, George (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Some geometric aspects of the calculus of variations in several independent variables

David Saunders (2010)

Communications in Mathematics

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This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.

Displaying similar documents to “Invariant variational problems on principal bundles and conservation laws”

Gl n ( R ) -invariant variational principles on frame bundles.

A new Lagrangian dynamic reduction in field theory

Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles

Equivariance, variational principles, and the Feynman integral.

Some geometric aspects of the calculus of variations in several independent variables

${Gl}_{n} (R)$ -invariant variational principles on frame bundles.