Details
| Original language | English |
|---|---|
| Article number | 407 |
| Number of pages | 13 |
| Journal | The European physical journal: Plus |
| Volume | 137 |
| Issue number | 3 |
| Early online date | 30 Mar 2022 |
| Publication status | Published - Mar 2022 |
Abstract
We revisit a newfound construction of rational electromagnetic knots based on the conformal correspondence between Minkowski space and a finite S3-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 S3 harmonics Yj;m,n, 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 j= 1. We demonstrate possible applications of our findings through some known previous results.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: The European physical journal: Plus, Vol. 137, No. 3, 407, 03.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Conserved charges for rational electromagnetic knots
AU - Hantzko, Lukas
AU - Kumar, Kaushlendra
AU - Picanço Costa, Gabriel
N1 - Funding Information: KK is grateful to Deutscher Akademischer Austauschdienst (DAAD) for the doctoral research grant 57381412. We thank Olaf Lechtenfeld for several insightful discussions and valuable suggestions.
PY - 2022/3
Y1 - 2022/3
N2 - We revisit a newfound construction of rational electromagnetic knots based on the conformal correspondence between Minkowski space and a finite S3-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 S3 harmonics Yj;m,n, 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 j= 1. We demonstrate possible applications of our findings through some known previous results.
AB - We revisit a newfound construction of rational electromagnetic knots based on the conformal correspondence between Minkowski space and a finite S3-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 S3 harmonics Yj;m,n, 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 j= 1. We demonstrate possible applications of our findings through some known previous results.
UR - http://www.scopus.com/inward/record.url?scp=85127446335&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2106.05952
DO - 10.48550/arXiv.2106.05952
M3 - Article
AN - SCOPUS:85127446335
VL - 137
JO - The European physical journal: Plus
JF - The European physical journal: Plus
SN - 2190-5444
IS - 3
M1 - 407
ER -