English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider the Pauli operator in $\mathbb R^3$ for magnetic fields in$L^{3/2}$ that decay at infinity as $|x|^{-2-\beta}$ with $\beta > 0$. In thiscase we are able to prove that the existence of a zero mode for this operatoris equivalent to a quantity $\delta(\mathbf B)$, defined below, being equal tozero. Complementing a result from [Balinsky, Evans, Lewis (2001)], this impliesthat for the class of magnetic fields considered, Sobolev, Hardy and CLRinequalities hold whenever the magnetic field has no zero mode.

A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields