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 Schrödinger 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.

中文翻译：

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一类多体费米子系统在$$ {\ mathbb {R}} ^ d $$ R d的Lieb–Robinson界和强连续动力学

我们介绍了\（{\ mathbb {R}} ^ d \）中一类费米子的UV正规化两体相互作用，并证明了Lieb-Robinson估计这类多体系统的动力学。为了朝这个结果迈进，我们还证明了Schrödinger算子的Lieb-Robinson型传播边界。我们应用传播边界来证明无限体积动力学的存在，作为CAR代数上的一个强连续的自同构群。