Advances in Theoretical and Mathematical Physics

Volume 16 (2012)

Number 1

Hamiltonian structure of gauge-invariant variational problems

Pages: 39 – 63



López Castrillón (Marco)

Masqué Muñoz (Jaime)


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.

Published 17 January 2013