Published Paper
Inserted: 9 mar 2020
Last Updated: 15 feb 2021
Journal: Commun. Math. Phys.
Pages: 30
Year: 2021
Doi: https://doi.org/10.1007/s00220-021-04013-1
Abstract:
We prove a classification result for ground state solutions of the critical Dirac equation on $\mathbb{R}^n$, $n\geq2$. By exploiting its conformal covariance, the equation can be posed on the round sphere $\mathbb{S}^n$ and the non-zero solutions at the ground level are given by Killing spinors, up to conformal diffeomorphisms. Moreover, such ground state solutions of the critical Dirac equation are also related to the Yamabe equation for the sphere, for which we crucially exploit some known classification results.
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