Geodesic
The Dirac operator with mass $m_0 \ge 0$: non-existence of zero modes and of threshold eigenvalues
Documenta mathematica, Tome 20 (2015), pp. 37-64.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A simple global condition on the potential is given which excludes zero modes of the massless Dirac operator. As far as local conditions at infinity are concerned, it is shown that at energy zero the Dirac equation without mass term has no non-trivial $L^2$-solutions at infinity for potentials which are either very slowly varying or decaying at most like $r^{-s}$ with $s \in (0,1)$. When a mass term is present, it is proved that at the thresholds there are again no such solutions when the potential decays at most like $r^{-s}$ with $s \in (0,2)$. In both situations the decay rate is optimal.
Classification : 35P15, 81Q10
Keywords: Dirac operators, virial theorem, threshold eigenvalue, zero mode 
@article{DOCMA_2015__20__a39,
     author = {Kalf, Hubert and Okaji, Takashi and Yamada, Osanobu},
     title = {The {Dirac} operator with mass $m_0 \ge 0$: non-existence of zero modes and of threshold eigenvalues},
     journal = {Documenta mathematica},
     pages = {37--64},
     publisher = {mathdoc},
     volume = {20},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a39/}
}
TY  - JOUR
AU  - Kalf, Hubert
AU  - Okaji, Takashi
AU  - Yamada, Osanobu
TI  - The Dirac operator with mass $m_0 \ge 0$: non-existence of zero modes and of threshold eigenvalues
JO  - Documenta mathematica
PY  - 2015
SP  - 37
EP  - 64
VL  - 20
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a39/
LA  - en
ID  - DOCMA_2015__20__a39
ER  - 
%0 Journal Article
%A Kalf, Hubert
%A Okaji, Takashi
%A Yamada, Osanobu
%T The Dirac operator with mass $m_0 \ge 0$: non-existence of zero modes and of threshold eigenvalues
%J Documenta mathematica
%D 2015
%P 37-64
%V 20
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a39/
%G en
%F DOCMA_2015__20__a39
Kalf, Hubert; Okaji, Takashi; Yamada, Osanobu. The Dirac operator with mass $m_0 \ge 0$: non-existence of zero modes and of threshold eigenvalues. Documenta mathematica, Tome 20 (2015), pp. 37-64. http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a39/