A topological theory of the electromagnetic field

✍ Scribed by Antonio F. Rañada

• Publisher: Springer
• Year: 1989
• Tongue: English
• Weight: 474 KB
• Volume: 18
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00401864

✦ Synopsis

It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field ~b which represents a map S 3 x R ~ S 2 and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions, characterized by a Hopf index equal to the linking number of any pair of magnetic lines. This allows the classification of the electromagnetic fields into homotopy classes, labeled by the value of the helicity. Although the model makes use of only c-number fields, the helicity always verifies S A" B d3r = na, n being an integer and a an action constant, which necessarily appears in the theory, because of reasons of dimensionality.