Generalization of Pauli’s exclusion principle via convex geometry

The Pauli exclusion principle is fundamentally important for our understanding of matter since it restricts the way electrons at zero temperature can distribute in space. At first sight, extending the respective physical theories for systems of N electrons beyond their ground state regime seems to be straightforward. Yet, in the form of the so-called one-body N-representability problem a non-trivial compatibility problem emerges. In our presentation, we explain how concepts of convex geometry allow us to solve that long-standing problem, leading to a hierarchy of generalized exclusion principle constraints. For this, we illustrate in particular how standard concepts of quantum many-body physics translate into convex geometry as lineups, threshold complexes, Gale posets and permutation-invariant polytopes.