Some remarks on Lagrangian and Poisson reduction for field theories

✍ Scribed by Marco Castrillón López; Jerrold E. Marsden

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 244 KB
• Volume: 48
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(03)00025-1

✦ Synopsis

Given a Hamiltonian system on a fiber bundle, the Poisson covariant formulation of the Hamilton equations is described. When the fiber bundle is a G-principal bundle and the Hamiltonian density is G-invariant, the reduction of this formulation is studied thus obtaining the analog of the Lie-Poisson reduction for field theories. The relation of this reduction with the Lagrangian reduction and the Lagrangian and Poisson reduction for electromagnetism are also analyzed.