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.