In this talk I will consider the dynamics of non-relativistic fermions in infinite volume in the continuum, interacting through a non-regularized pair potential. Employing methods developed by Buchholz in the framework of resolvent algebras for bosons, I will show how the CAR algebra can be extended such that the dynamics acts as a group of $*$-automorphisms, which are continuous in time in all sectors of fixed particle numbers. Using the subalgebra generated by time-averages, one obtains a $C^*$-dynamical system which is dense in the extended CAR algebra with respect to the seminorms of fixed particle numbers. The discussion is significantly shorter than in the bosonic case and provides a potential framework for discussing KMS states.