Abstract
It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field ϕ which represents a map S3×R→S2 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 ∫ A·Bd3r=nα, n being an integer and α an action constant, which necessarily appears in the theory, because of reasons of dimensionality.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.