A Groupoid Approach to Interacting Fermions

Abstract

We consider the algebra Σ ˙ (L) generated by the inner-limit derivations over the GICAR algebra of a fermion gas populating an aperiodic Delone set L. Under standard physical assumptions such as finite interaction range, Galilean invariance of the theories and continuity with respect to the deformations of the aperiodic lattices, we demonstrate that the image of Σ ˙ (L) through the Fock representation can be completed to a groupoid-solvable pro-C∗-algebra. Our result is the first step towards unlocking the K-theoretic tools available for separable C∗-algebras for applications in the context of interacting fermions.