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| Let $C\to M$ be the bundle of connections of a principal bundle on $M$.
Solutions to Hamilton-Cartan equations for a first order gauge-invariant
Lagrangian density on $C$ are not equivalent to solutions of the Euler-Lagrange
equations. In this talk it is proved that, under a weak condition of regularity, the set
of Hamiltonian solutions admits the structure of an affine bundle over the set
of solutions of the Lagrangian problem. This structure is also studied for the
Jacobi fields and for the moduli space of extremals. |
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