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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 thisclass of many-body systems. As a step toward this result, we also prove apropagation bound of Lieb-Robinson type for Schr\"odinger operators. We applythe propagation bound to prove the existence of infinite-volume dynamics as astrongly continuous group of automorphisms on the CAR algebra.

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