TDDFT in Phase-Space

We explore the possibility of a density-functional theory in phase-space, where the basic variable is a phase-space density rather than the usual coordinate-space density. In this way information about the momentum distribution is directly captured, rather than being hidden in the form of the exchange-correlation functionals, which often complicates the functional, making it hard to approximate. We give examples to motivate this approach, and discuss initial stages in the development of the functionals.