André Carlzon Laestadius: Hohenberg-Kohn Theorems in the Presence of Magnetic Field

For a quantum-mechanical system of interacting electrons, I will here examine Hohenberg-Kohn theorems for Current Density Functional Theory, that is, generalizations of the classical Hohenberg-Kohn theorem that includes both electric and magnetic fields. In the Vignale and Rasolt formulation that uses the paramagnetic current density, I will address the issue of degenerate ground-states and prove that the ensemble-representable particle and paramagnetic current density determine the degenerate ground-states. I will moreover prove the existence of a positive wavefunction that is the ground-state of infinitely many different Hamiltonians.