Abstract
We exhibit a close relation between vortex configurations on the 2sphere and magnetic zeromodes of the Dirac operator on (Formula presented.) which obey an additional nonlinear equation. We show that both are best understood in terms of the geometry induced on the 3sphere via pullback of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth formula for squareintegrable magnetic zeromodes in terms of two homogeneous polynomials in two complex variables.
Original language  English 

Pages (fromto)  135 
Number of pages  35 
Journal  Letters in Mathematical Physics 
Early online date  7 Nov 2017 
DOIs  
Publication status  Epub ahead of print  7 Nov 2017 
Keywords
 Cartan geometry
 Dirac operator
 Magnetic zeromodes
 Vortex equations
ASJC Scopus subject areas
 Statistical and Nonlinear Physics
 Mathematical Physics
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Bernd Johannes Schroers
 School of Mathematical & Computer Sciences  Professor
 School of Mathematical & Computer Sciences, Mathematics  Professor
Person: Academic (Research & Teaching)