A many-body theory is formulated for an inhomogeneous, interacting electron
gas with electronic current. Electronic current is induced by a constraint
condition imposed as a vector Lagrange multiplier. Constrained minimizatio
n of the total energy on the manifold of an arbitrary constant current lead
s to a many-electron Schrodinger equation with a complex, momentum-dependen
t potential. Constant current Hartree-Fock and Kohn-Sham approximations are
formulated within the method and application to transport for quantum wire
s is developed. (C) 2001 Elsevier Science B.V. All rights reserved.