A new construction of rational electromagnetic knots

Abstract

We set up a correspondence between solutions of the Yang-Mills equations on $\mathbb{R}\times S^3$ 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.

1+8 pages, 4 figures; v2: map between S^3-cylinder and Minkowski space clarified, published version

References in corpus (1)

• Solutions to Yang-Mills equations on four-dimensional de Sitter space

Cited by in corpus (12)

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• Yang-Mills solutions on Minkowski space via non-compact coset spaces
• Numerical simulation of knotted solutions for Maxwell equations
• Nonlinear dynamics of a charged particle in a strong non-null knot wave background
• Finsler Geometries from Topological Electromagnetism
• A low-energy limit of Yang-Mills theory on de Sitter space
• Gravitoelectromagnetic knot fields
• Conserved charges for rational electromagnetic knots
• Are Maxwell knots integrable?
• Trajectories of charged particles in knotted electromagnetic fields
• Classification of all constant solutions of $\mathrm{SU}(2)$ Yang-Mills equations with arbitrary current in pseudo-Euclidean space ${\mathbb{R}}^{p,q}$
• Knots and the Maxwell Equations