Aspects of relativistic Hamiltonian physics

D'Avignon, Eric Cavell
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This dissertation presents various new results in relativistic Hamiltonian plasma physics. It begins with an overview of Hamiltonian physics, with an emphasis on noncanonical brackets, and presents various nonrelativistic systems to be generalized later on. There then follows an exposition on action principles for Hall and Extended MHD, which allow the derivation of the noncanonical Hamiltonian brackets for those systems. I next discuss the transition to relativistic Hamiltonian systems, and the special difficulties that arise in this step. A detailed exploration of relativistic Hamiltonian MHD follows, using a novel bracket formulation. This chapter also investigates alternative brackets, gauge degeneracies, and Casimir invariants. Next I lay out the connection between Lagrangian and Eulerian MHD (both in Hamiltonian forms), and present some early work on a bracket-based formulation of the relativistic Navier-Stokes equation. The next chapters develop various results using an antisymmetric relativistic spin tensor, and several unexpected and intriguing physical consequences of the Jacobi identity. I conclude with a program of future research and several useful appendices.