A local-scaling current density functional theory

The local-scaling density functional theory [J. Phys. Soc. Jpn. 72 (2003) 1926; J. Phys. Soc. Jpn. 73 (2004) 882] is extended to that for systems in magnetic fields of arbitrary strength. Formally exact expressions of the exchange-correlation scalar potential and the vector one are derived. The differential virial theorem provided by Holas and March [Phys. Rev. A 56 (1997) 4595] is also obtained, whose exchange-correlation part is satisfied by the present expressions of exchange-correlation potentials. Furthermore, the integral form of the virial theorem derived by Erhard and Gross [Phys. Rev. A 53 (1996) R5] is discussed briefly, too.