Using a unified approach employing a homogeneous Lippmann-Schwinger-type equation satisfied by resonance functions and basic facts on Riesz potentials, we discuss the absence of threshold resonances for Dirac and Schrödinger operators with sufficiently short-range interactions in general space dimensions.More specifically, assuming a sufficient power law decay of potentials, we derive the absence of zero-energy resonances for massless Dirac operators in space dimensions $ n \geqslant 3 $, the absence of resonances at $ \pm m $ for massive Dirac operators (with mass $ m > 0 $) in dimensions $ n \geqslant 5 $, and recall the well-known case of absence of zero-energy resonances for Schrödinger operators in dimension $ n \geqslant 5 $.

中文翻译：

---

对于Schrödinger和Dirac算子没有阈值共振

使用统一的方法，使用共振函数和Riesz势的基本事实满足的齐次Lippmann-Schwinger型方程，我们讨论了Dirac和Schrödinger算子在总体空间维度上具有足够短程相互作用的阈值共振的缺失。假设势有足够的幂律衰减，我们推导出空间量$ n \ geqslant 3 $的无质量Dirac算子没有零能量共振，大型Dirac算子（质量为$ m> 0 $）在维$ n \ geqslant 5 $中，并回想一下在$ n \ geqslant 5 $中Schrödinger算子不存在零能量共振的著名情况。