Corpus ID: 234096235

# The limiting absorption principle for massless Dirac operators, properties of spectral shift functions, and an application to the Witten index of non-Fredholm operators

@inproceedings{Carey2021TheLA,
title={The limiting absorption principle for massless Dirac operators, properties of spectral shift functions, and an application to the Witten index of non-Fredholm operators},
author={Alan L. Carey and Fritz Gesztesy and Galina Levitina and Roger Nichols and Fedor Sukochev and Dmitriy Zanin},
year={2021}
}
We derive a limiting absorption principle on any compact interval in $\mathbb{R} \backslash \{0\}$ for the free massless Dirac operator, $H_0 = \alpha \cdot (-i \nabla)$ in $[L^2(\mathbb{R}^n)]^N$, $n \geq 2$, $N=2^{\lfloor(n+1)/2\rfloor}$, and then prove the absence of singular continuous spectrum of interacting massless Dirac operators $H = H_0 +V$, where $V$ decays like $O(|x|^{-1 - \varepsilon})$. Expressing the spectral shift function $\xi(\,\cdot\,; H,H_0)$ as normal boundary values of… Expand