Density-functional theory in strong magnetic fields

We formulate the current-density--functional theory for systems in arbitrarily strong magnetic fields. A set of self-consistent equations comparable to the Kohn-Sham equations for ordinary density-functional theory is derived, and proved to be gauge invariant and to satisfy the continuity equation. We prove that the exchange-correlation energy functional Eₗ₂₍, j₏ n (r) is the density and j₏ (r) is the ``paramagnetic'' current density depends on the current via the combination (r) =j₏ (r) /n (r). An explicit formula for Eₗ₂ is derived, which is local in (r).