Variáveis dinâmicas não comutativas em magnetohidrodinâmica e método Faddeev-Jackiw aplicado à magnetohidrodinâmica relativística

Abstract

Magnetohydrodynamics (MHD) describes the behavior of a charged fluid embedded in a magnetic field. Such systems, when electrical conductivity and frequency of the external electromagnetic field belongs to a certain range of valeus, present a particular wave behavior. This is manifested through the H. Alfvén’s waves [1]. It is noteworthy to mention that, for both fluido mechanics and Magnetohydrodynamics, when analyzed in a noncommutative space, they present paculiar characteristics. In this work, an algebra of noncommutative velocities was built for the MHD, where the noncommutative version of the Navier-Stokes equation was obtained, the variation of mechanical energy was analized together with the coupling between the vorticity and tha magnetic field, and studied the variation of the circulation, where each of the terms were analyzed. We see that these, due to the presence of the noncommutative parameter, can act as a source of vorticity. To obtain the equations for the noncommutative MHD, a new Lagrangian was introduced, which allowed the construction of a Hamiltonian for the MHD. This Hamiltonian, together with the new noncommutative simplectic structure, gives rise to a noncommutative dynamics for the MHD. At the end, the symplectic method was applied to a relativistic ideal charged fluid, composed by massive particles. For this system, the symplectic matrix was constructed and the generalized parentheses were obtained.