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A new Lagrangian dynamic reduction in field theory. (English) Zbl 1404.58029

Summary: 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 invariant.

MSC:

58E30 Variational principles in infinite-dimensional spaces
70H03 Lagrange’s equations
70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
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References:

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