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Title: Wedge reversion antisymmetry and 41 types of physical quantities in arbitrary dimensions
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.
Award ID(s):
Publication Date:
Journal Name:
Acta Crystallographica Section A Foundations and Advances
Page Range or eLocation-ID:
318 to 327
Sponsoring Org:
National Science Foundation
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