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An introduction to relativistic electrodynamics: Part II: Calculus with complex 4-vectors
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)ORCID iD: 0000-0001-7838-1307
2018 (English)Report (Other academic)
Abstract [en]

The conventional way of introducing relativity when teaching electrodynamics is to leave Gibbs' vector calculus for a more general tensor calculus. This sudden change of formalism can be quite problematic for the students and we therefore in this two-part paper consider alternate approaches. The algebra  of 2-by-2 complex matrices (sometimes presented in the form of Clifford algebra or complex quaternions) may be used for spinor related formulations of special relativity and electrodynamics. In this Part II we use this algebraic structure but with notations that fits in with the formalism of Part I. Each observer  defines a product on the space of complex 4-vectors  so that  becomes an algebra isomorphic to  with  as algebra unit. The spacetime geometric equations of Part I become complex (spinor related) equations where the antisymmetric 4-dyadics have been replaced by complex 3-vectors, i.e., by elements in . For example, instead of the electromagnetic dyadic field  we now have the complex field variable . Some linear algebra together with the formalism of Gibbs' vector calculus (trivially allowing for complex 3-vectors) is sufficient for dealing with the equations in their complex form.

Place, publisher, year, edition, pages
2018. , p. 7
Keywords [en]
electrodynamics, special relativity, coordinate-free calculus, spinors
National Category
Other Physics Topics
Research subject
Physics
Identifiers
URN: urn:nbn:se:umu:diva-152751OAI: oai:DiVA.org:umu-152751DiVA, id: diva2:1257612
Available from: 2018-10-22 Created: 2018-10-22 Last updated: 2018-10-25

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Larsson, JonasLarsson, Karl

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf