Introductions to Density Functional Theory (DFT) usually discuss the Hohenberg–Kohn theorems which prove that there exist universal functionals of density that can be used to determine ground state properties of a system. This has extensions for degenerate ground states, or incorporating spin, or magnetic interactions, or even time dependent systems and excited states.
But all these seem to arrive at the proof by discussing a system in terms of a fixed number of particles, and the wavefunction in terms of the particle positions. This means DFT has its basis in non-relativistic fixed-particle-number quantum mechanics.
Is it possible for density functional theory to also be applied to a quantum field theory, such as QED or QCD?