| Summary: | We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional Density Functional Theory and Current-Density Functional Theory (CDFT). In the intermediate theory, which we term LDFT, the basic variables are the den- sity, the canonical momentum, and the paramagnetic contribution to the magnetic moment. Both a constrained-search formulation and a convex formulation in terms of Legendre–Fenchel transfor- mations are constructed. Many theoretical issues in CDFT find simplified analogues in LDFT. We prove results concerning N-representability, Hohenberg–Kohn-like mappings, existence of minimiz- ers in the constrained-search expression, and a restricted analogue to gauge invariance. The issue of additivity of the energy over non-interacting subsystems, which is qualitatively different in LDFT and CDFT, is also discussed.
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