Cargando…
Magnetic zero-modes, vortices and Cartan geometry
We exhibit a close relation between vortex configurations on the 2-sphere and magnetic zero-modes of the Dirac operator on [Formula: see text] which obey an additional nonlinear equation. We show that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the roun...
| Autores principales: | , |
|---|---|
| Formato: | Online Artículo Texto |
| Lenguaje: | English |
| Publicado: |
Springer Netherlands
2017
|
| Materias: | |
| Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5869901/ https://www.ncbi.nlm.nih.gov/pubmed/29606790 http://dx.doi.org/10.1007/s11005-017-1023-2 |
| Sumario: | We exhibit a close relation between vortex configurations on the 2-sphere and magnetic zero-modes of the Dirac operator on [Formula: see text] which obey an additional nonlinear equation. We show that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth formula for square-integrable magnetic zero-modes in terms of two homogeneous polynomials in two complex variables. |
|---|