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Conservation laws for symmetrised electromagnetic equations with a dual Ohm's law
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
Responsible organisation
2007 (English)Conference paper, Presentation (Refereed)
Abstract [en]

In all areas of physics, conservation laws are essential since they allow us to draw conclusions of our physical system under study in an indirect but efficient way. Electrodynamics, in terms of the standard Maxwell electromagnetic equations for fields in vacuum, exhibit a rich set of symmetries to which conserved quantities are associated. We have derived conservation laws for Dirac's symmetric version of the Maxwell-Lorentz microscopic equations, allowing magnetic charges and magnetic currents, where the latter, just as electric currents, are assumed to be described by a linear relationship between the field and the current, i.e. an Ohm's law. We find that when we use the method of Ibragimov to construct the conservation laws, they will contain two new adjoint vector fields which fulfil Maxwell-like equations. In particular, we obtain conservation laws for the electromagnetic field which are nonlocal in time.

Place, publisher, year, edition, pages
Karlskrona, Sweden, 2007.
Keyword [en]
Conservation laws, Maxwell electromagnetic equations for fields in vacuum
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:bth-8718Local ID: oai:bth.se:forskinfo635747B58EC2FE42C12573C900334809OAI: oai:DiVA.org:bth-8718DiVA: diva2:836470
Conference
International conference MOGRAN 11, Karlskrona
Available from: 2012-09-18 Created: 2008-01-07 Last updated: 2015-09-28Bibliographically approved

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Ibragimov, Nail H.Khamitova, Raisa
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