https://doi.org/10.1140/epjp/s13360-022-02563-4
Regular Article
Conserved charges for rational electromagnetic knots
Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany
b
kaushlendra.kumar@itp.uni-hannover.de
Received:
13
December
2021
Accepted:
6
March
2022
Published online:
30
March
2022
We revisit a newfound construction of rational electromagnetic knots based on the conformal correspondence between Minkowski space and a finite 
-cylinder. We present here a more direct approach for this conformal correspondence based on Carter–Penrose transformation that avoids a detour to de Sitter space. The Maxwell equations can be analytically solved on the cylinder in terms of harmonics 
, which can then be transformed into Minkowski coordinates using the conformal map. The resultant “knot basis” electromagnetic field configurations have non-trivial topology in that their field lines form closed knots. We consider finite, complex linear combinations of these knot-basis solutions for a fixed spin j and compute all the 15 conserved Noether charges associated with the conformal group. We find that the scalar charges either vanish or are proportional to the energy. For the non-vanishing vector charges, we find a nice geometric structure that facilitates computation of their spherical components as well. We present analytic results for all charges for up to 
. We demonstrate possible applications of our findings through some known previous results.
© The Author(s) 2022
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