Thinking outside the box: The uniform electron gas on a hypersphere

We discuss alternative homogeneous electron gas systems in which a finite number n of electrons are confined to a D-dimensional sphere. We derive the first few terms of the high-density (r _s → 0, where r _s is the Seitz radius) energy expansions for these systems and show that, in the thermodynamic limit (n → ∞), these terms become identical to those of D-dimensional jellium.