A new construction of rational electromagnetic knots
Abstract
We set up a correspondence between solutions of the Yang-Mills equations on R ×S3 and in Minkowski spacetime via de Sitter space. Some known Abelian and non-Abelian exact solutions are rederived. For the Maxwell case we present a straightforward algorithm to generate an infinite number of explicit solutions, with fields and potentials in Minkowski coordinates given by rational functions of increasing complexity. We illustrate our method with a nontrivial example.
- Publication:
-
Physics Letters A
- Pub Date:
- June 2018
- DOI:
- 10.1016/j.physleta.2018.04.027
- arXiv:
- arXiv:1711.11144
- Bibcode:
- 2018PhLA..382.1528L
- Keywords:
-
- Electromagnetic knots;
- Maxwell equations;
- Yang-Mills on conformally flat spacetime;
- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 1+8 pages, 4 figures