On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets

Cristel Chandre (1, 2) , Loïc de Guillebon (1, 2) , Aurore Back (1, 2) , Emanuele Tassi (1, 2) , Philip Morrison (3)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - Ex E8 Dynamique non linéaire
3 IFS - Institute for Fusion Studies

The role of projectors associated with Poisson brackets of constrained Hamiltonian systems is analyzed. Projectors act in two instances in a bracket: in the explicit dependence on the variables and in the computation of the functional derivatives. The role of these projectors is investigated by using Dirac's theory of constrained Hamiltonian systems. Results are illustrated by three examples taken from plasma physics: magnetohydrodynamics, the Vlasov-Maxwell system, and the linear two-species Vlasov system with quasineutrality.

Domaines: Dynamique Chaotique [nlin.CD]; Dynamique des Fluides [physics.flu-dyn]; Physique des plasmas [physics.plasm-ph]

Cristel Chandre, Loïc de Guillebon, Aurore Back, Emanuele Tassi, Philip Morrison. On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets. Journal of Physics A: Mathematical and Theoretical, 2013, 46 (12), pp.125203. ⟨10.1088/1751-8113/46/12/125203⟩. ⟨hal-00696091⟩