Hamiltonian structure of gauge-invariant variational problems

Abstract

Let $C \to M$ be the bundle of connections of a principal bundle on $M$. The solutions to Hamilton–Cartan equations for a gauge-invariant Lagrangian density $\Lambda$ 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 $\Lambda$. This structure is also studied for the Jacobi fields and for the moduli space of extremals.