On Absence of Threshold Resonances for Schrodinger and Dirac Operators

Abstract

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 Schrodinger 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 $n\ge 3$, the absence of resonances at $\pm m$ for massive Dirac operators (with mass $m>0$) in dimensions $n\ge 5$, and recall the well-known case of absence of zero-energy resonances for Schrödinger operators in dimension $n\ge 5$.

34 pages. arXiv admin note: substantial text overlap with arXiv:2105.03024

References in corpus (3)

• Dirac-Sobolev inequalities and estimates for the zero modes of massless Dirac operators
• A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields
• Zero modes for the magnetic Pauli operator in even-dimensional Euclidean space