André Carlzon Laestadius: Hohenberg-Kohn theory in the presence of magnetic field

In the first attempt to generalize the Hohenberg-Kohn theory to include magnetic fields in the formalism, Vignale and Rasolt tried to prove a Hohenberg-Kohn using the particle and paramagnetic current density. Later, however, Vignale and Capelle noted that the proof was in error. Indeed, a wavefunction can be the ground-state of two different Hamiltonians, a complication not present in the classical Hohenberg-Kohn theory. In this talk some recent progress in Current Density Functional Theory will be explored. This includes: (i) general one-to-one correspondence between the set of ground-states and particle and paramagnetic current density, (ii) extension to N-representable densities and (iii) generalized Kohn-Sham theory.