Hamiltonian structure of gauge-invariant variational problems

Abstract

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.