Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids

Details Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids

2009-03-25

arxiv.org/abs/0903.4287v1

Journal of Symplectic Geometry, 6 (2) 2008, 189-237

Physics

Mathematical Physics

Scientific paper

The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are determined. Using a Kaluza-Klein point of view, the equations of motion are obtained by Lagrangian and Poisson reductions associated to the automorphism group of a principal bundle. As a consequence of the Lagrangian approach, a Kelvin-Noether theorem is obtained. The Hamiltonian formulation determines a non-canonical Poisson bracket associated to these equations.

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