A topological theory of the electromagnetic field

DOI10.1007/BF00401864zbMath0687.57015OpenAlexW1498029772MaRDI QIDQ1263135

Antonio F. Rañada

Publication date: 1989

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00401864

zbMATH Keywords

linearizationhomotopy classeselectromagnetic fieldscalar fieldhelicityquantum structureHopf indexlinking number of magnetic linesmaps from \(S^ 3\times {\mathbb{R}}\) to \(S^ 2\)Maxwell equations in vacuum

Mathematics Subject Classification ID

Homotopy groups, general; sets of homotopy classes (55Q05) Quantum field theory; related classical field theories (81T99) Differential topology (57R99) Applications of PDEs on manifolds (58J90) Electromagnetic theory (general) (78A25)

Related Items (34)

Quasipositive links and electromagnetism ⋮ Linked and knotted beams of light, conservation of helicity and the flow of null electromagnetic fields ⋮ Optical knots and contact geometry. I: From Arnol'd inequality to Ranada's dyons ⋮ Exchange of helicity in a knotted electromagnetic field ⋮ Generalized helicity and Beltrami fields ⋮ On spacetime foliations and electromagnetic knots ⋮ Trajectories of charged particles in knotted electromagnetic fields ⋮ Lagrangian Formulation, Generalizations and Quantization of Null Maxwell's Knots ⋮ Magnetic surface topology in decaying plasma knots ⋮ Knotted solutions, from electromagnetism to fluid dynamics ⋮ Optical knots and contact geometry. II: From Ranada dyons to transverse and cosmetic knots ⋮ Effects of twist on the evolution of knotted magnetic flux tubes ⋮ Spacetime foliations, quaternions and knotted light ⋮ When do knots in light stay knotted? ⋮ Fluid-electromagnetic helicities and knotted solutions of the fluid-electromagnetic equations ⋮ Collision of two hopfions ⋮ On the existence of the field line solutions of the Einstein–Maxwell equations ⋮ On rational electromagnetic fields ⋮ Electromagnetic knots ⋮ Time evolving potentials for electromagnetic knots ⋮ Beyond skyrmions: review and perspectives of alternative magnetic quasiparticles ⋮ Geometric and quantum properties of charged particles in monochromatic electromagnetic knot background ⋮ Knotted solutions for linear and nonlinear theories: electromagnetism and fluid dynamics ⋮ Stable knots and links in electromagnetic fields ⋮ Relation between stereographic projection and concurrence measure in bipartite pure states ⋮ Knots in electromagnetism ⋮ Helicity and vortex generation ⋮ A new construction of rational electromagnetic knots ⋮ Knotted surfaces as vanishing sets of polynomials ⋮ Anti-Self-dual spacetimes, gravitational instantons and knotted zeros of the Weyl tensor ⋮ Spin-orbital momentum decomposition and helicity exchange in a set of non-null knotted electromagnetic fields ⋮ On the fibration defined by the field lines of a knotted class of electromagnetic fields at a particular time ⋮ Interplay of topology and quantization: topological energy quantization in a cavity ⋮ Deformed hopfion-Rañada knots in ModMax electrodynamics

Cites Work

• Construction of nonlinear sigma-models in two and higher space- dimensions
• Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche
• A THEOREM ON FORCE-FREE MAGNETIC FIELDS
• Significance of Electromagnetic Potentials in the Quantum Theory
• Quantal phase factors accompanying adiabatic changes
• Some developments in the theory of turbulence
• Quantised singularities in the electromagnetic field,
• An Expression of Hopf's Invariant as an Integral

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