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Dimensionally dependent identities and the Lanczos potential
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
2000 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

To antisymmetrize over more indices than the number of dimensions gives a dimensionally dependent identity. In this thesis such identities for tensors, spinors and matrices are discussed and some new results are presented which generalise earlier results of Lovelock. The relevance of such identities in a systematic study of syzygies of scalar invariants is also illustrated.

A Lanczos potential is a potential of the Weyl curvature tensor or a tensor with the same algebraic symmetries, i.e. a Weyl candidate tensor. In this thesis we derive a wave equation for the Lanczos potential in arbitrary gauges and in arbitrary dimensions with arbitrary signatures. We are able to see that the form of the wave equation for the Lanczos potential, which is very simple in four dimensions, is much more complicated in higher dimensions. Furthermore, although it is known that a Lanczos potential always exists in four dimensions, we show that the Lanczos potential does not always exist in n dimensions for n ≥ 5. Necessary conditions for Weyl candidate tensors to have a Lanczos potential are also derived.

The computer program Tensign, developed for the calculations in this thesis, is discussed.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2000. , p. 75
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 828
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-145923Local ID: LiU-TEK-LIC-2000:24ISBN: 9172197315 (print)OAI: oai:DiVA.org:liu-145923DiVA, id: diva2:1200071
Presentation
2000-06-08, Beurling, Campus Valla, Linköping, Sweden, 15:15 (Swedish)
Opponent
Available from: 2018-04-23 Created: 2018-04-23 Last updated: 2018-11-15Bibliographically approved

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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  • text
  • asciidoc
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