Conservation laws for symmetrised electromagnetic equations with a dual Ohm's law

Document type: Conference Presentations
Peer reviewed: Yes
Author(s): Nail H. Ibragimov, Raisa Khamitova, Bo Thidé
Title: Conservation laws for symmetrised electromagnetic equations with a dual Ohm's law
Conference name: International conference MOGRAN 11
Year: May 27-June 2, 2007
City: Karlskrona, Sweden
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. Mathematics and Science (Sektionen för teknik – avd. för matematik och naturvetenskap)
School of Engineering S- 371 79 Karlskrona
+46 455 38 50 00
http://www.tek.bth.se/
Authors e-mail: nib@bth.se, rkh@bth.se
Language: English
Abstract: 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.
Subject: Mathematics\Analysis
Keywords: Conservation laws, Maxwell electromagnetic equations for fields in vacuum
Edit