Hamiltonian structure of gauge-invariant variational problems

Let C → M be the bundle of connections of a principal bundle on M. The solutions to Hamilton–Cartan equations for a gauge-invariant Lagrangian density Λ on C satisfying a weak condition of regularity, are shown to admit an affine fibre-bundle structure over the set of solutions to Euler–Lagrange equations for Λ. This structure is also studied for the Jacobi fields and for the moduli space of extremals.

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Published 17 January 2013