On linearity of separating multi-particle differential Schr\"odinger operators for identical particles

Abstract

We show that hierarchies of differential Schroedinger operators for identical particles which are separating for the usual (anti-)symmetric tensor product, are necessarily linear, and offer some speculations on the source of quantum linearity.Comment: As accepted by Journal of Mathematical Physics. Original title "Separating multi-particle differential Schroedinger operators for identical particles are necessarily linear". Some new discussion and references. Main result unchanged. Uses RevTeX 4, 9 page