Hamiltonian Structure of Gauge-Invariant Variational Problems

2010/04/27 by Lopez, Marco Castrillon, Masque, Jaime Munoz
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1004.4923

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.

Related

• Reduction in principal fiber bundles: covariant Euler-Poincare equations
• Lagrangian and Hamiltonian Formalism for Constrained Variational Problems
• Second-order Lagrangians admitting a first-order Hamiltonian formalism
• Structure of Gauge-Invariant Lagrangians
• Diffeomorphism-invariant Covariant Hamiltonians of a pseudo-Riemannian Metric and a Linear Connection