Publication

Poisson reduction and the Hamiltonian structure of the Euler-Yang-Mills equations

Tudor Ratiu, François Gay-Balmaz
2008
Conference Papers

Abstract

The problem treated here is to find the Hamiltonian structure for an ideal gauge-charged fluid. Using a Kaluza-Klein point of view, we obtain the non-canonical Poisson bracket and the motion equations by a Poisson reduction involving the automorphism group of a principal bundle.

Official source

https://infoscience.epfl.ch/entities/publication/14b089b2-af06-42bd-a426-c36032744e40

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Tudor Ratiu, François Gay-Balmaz
2008
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/14b089b2-af06-42bd-a426-c36032744e40

About this result

Related concepts (32)

Hamiltonian mechanics

Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics.

Poisson bracket

In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems.

Principal bundle

In mathematics, a principal bundle is a mathematical object that formalizes some of the essential features of the Cartesian product of a space with a group . In the same way as with the Cartesian product, a principal bundle is equipped with An action of on , analogous to for a product space. A projection onto . For a product space, this is just the projection onto the first factor, . Unlike a product space, principal bundles lack a preferred choice of identity cross-section; they have no preferred analog of .

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