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 E_xc[n,j_p] [n(r) is the density and j_p(r) is the ``paramagnetic'' current density] depends on the current via the combination ν(r)=∇×[j_p(r)/n(r)]. An explicit formula for E_xc is derived, which is local in ν(r).