Forty-one 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, time-reversal, and a third that is introduced here, namely, wedge reversion. It is shown that the traits of “axiality” and “chirality” are not good basis for extending the classification of multivectors into arbitrary dimensions, and that introducing wedge reversion 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.

Ref: Acta Cryst. (2020). A76, 318–327