Details
| Original language | English |
|---|---|
| Article number | 126445 |
| Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |
| Volume | 384 |
| Issue number | 23 |
| Early online date | 30 Mar 2020 |
| Publication status | Published - 17 Aug 2020 |
Abstract
We employ a recently developed method for constructing rational electromagnetic field configurations in Minkowski space to investigate several properties of these source-free finite-action Maxwell (“knot”) solutions. The construction takes place on the Penrose diagram but uses features of de Sitter space, in particular its isometry group. This admits a classification of all knot solutions in terms of S3 harmonics, labeled by a spin 2j∈N0, which in fact provides a complete “knot basis” of finite-action Maxwell fields. We display a j=1 example, compute the energy for arbitrary spin-j configurations, derive a linear relation between spin and helicity and characterize the subspace of null fields. Finally, we present an expression for the electromagnetic flux at null infinity and demonstrate its equality with the total energy.
Keywords
- de Sitter space, Electromagnetic knots, Hyperspherical harmonics, Maxwell equations
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 384, No. 23, 126445, 17.08.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On rational electromagnetic fields
AU - Kumar, Kaushlendra
AU - Lechtenfeld, Olaf
N1 - Funding information: K.K. is grateful to Deutscher Akademischer Austauschdienst (DAAD) for the doctoral research grant 57381412 . He thanks Gleb Zhilin for useful discussions. O.L. benefited from conversations with Harald Skarke. Mathematica verification by Colin Becker and help with Fig. 2 by Till Bargheer are acknowledged. K.K. is grateful to Deutscher Akademischer Austauschdienst (DAAD) for the doctoral research grant 57381412. He thanks Gleb Zhilin for useful discussions. O.L. benefited from conversations with Harald Skarke. Mathematica verification by Colin Becker and help with Fig. 2 by Till Bargheer are acknowledged.
PY - 2020/8/17
Y1 - 2020/8/17
N2 - We employ a recently developed method for constructing rational electromagnetic field configurations in Minkowski space to investigate several properties of these source-free finite-action Maxwell (“knot”) solutions. The construction takes place on the Penrose diagram but uses features of de Sitter space, in particular its isometry group. This admits a classification of all knot solutions in terms of S3 harmonics, labeled by a spin 2j∈N0, which in fact provides a complete “knot basis” of finite-action Maxwell fields. We display a j=1 example, compute the energy for arbitrary spin-j configurations, derive a linear relation between spin and helicity and characterize the subspace of null fields. Finally, we present an expression for the electromagnetic flux at null infinity and demonstrate its equality with the total energy.
AB - We employ a recently developed method for constructing rational electromagnetic field configurations in Minkowski space to investigate several properties of these source-free finite-action Maxwell (“knot”) solutions. The construction takes place on the Penrose diagram but uses features of de Sitter space, in particular its isometry group. This admits a classification of all knot solutions in terms of S3 harmonics, labeled by a spin 2j∈N0, which in fact provides a complete “knot basis” of finite-action Maxwell fields. We display a j=1 example, compute the energy for arbitrary spin-j configurations, derive a linear relation between spin and helicity and characterize the subspace of null fields. Finally, we present an expression for the electromagnetic flux at null infinity and demonstrate its equality with the total energy.
KW - de Sitter space
KW - Electromagnetic knots
KW - Hyperspherical harmonics
KW - Maxwell equations
UR - http://www.scopus.com/inward/record.url?scp=85082779278&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2002.01005
DO - 10.48550/arXiv.2002.01005
M3 - Article
AN - SCOPUS:85082779278
VL - 384
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 23
M1 - 126445
ER -