Wedge reversion antisymmetry and 41 types of physical quantities in arbitrary dimensions

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It is shown that there are 41 types of multivectors representing physical quantities in non-relativistic physics in arbitrary dimensions within the formalism of Clifford algebra. The classification is based on the action of three symmetry operations on a general multivector: spatial inversion, 1, time-reversal, 1′, and a third that is introduced here, namely wedge reversion, 1. It is shown that the traits of 'axiality' and 'chirality' are not good bases for extending the classification of multivectors into arbitrary dimensions, and that introducing 1 would allow for such a classification. Since physical properties are typically expressed as tensors, and tensors can be expressed as multivectors, this classification also indirectly classifies tensors. Examples of these multivector types from non-relativistic physics are presented.

Original languageEnglish (US)
Pages (from-to)318-327
Number of pages10
JournalActa Crystallographica Section A: Foundations and Advances
StatePublished - May 1 2020

All Science Journal Classification (ASJC) codes

  • Structural Biology
  • Biochemistry
  • Materials Science(all)
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Inorganic Chemistry


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