Hamiltonian and action principle formalisms for spin-1/2 magnetohydrodynamics

A Hamiltonian and Action Principle formulation of spin-1/2 magnetohydrodynamics is presented via a first-principles derivation of the underlying Lagrangian, and the associated Hamiltonian. The derivation invokes the notion of "frozen-in" constraints, symmetry breaking, and similarities with Ginzburg-Landau theory to arrive at the relevant terms in the Hamiltonian. The model thus obtained includes the effects of spin and other quantum corrections and is shown to be in full agreement with existent models in the literature. It is also indicated how two-fluid effects, gyroviscosity, and anisotropic pressure can be included in the model, in addition to incorporating higher-order (nonlinear) quantum spin corrections. An interesting analogy with the theory of liquid crystals is also highlighted