Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in ${\mathbb{R}}^d$

We introduce a class of UV-regularized two-body interactions for fermions in ${\mathbb{R}}^d$ and prove a Lieb-Robinson estimate for the dynamics of this class of many-body systems. As a step toward this result, we also prove a propagation bound of Lieb-Robinson type for Schr"odinger operators. We apply the propagation bound to prove the existence of infinite-volume dynamics as a strongly continuous group of automorphisms on the CAR algebra.