Forty-One Types of Physical Quantities in Arbitrary Dimensions

TL;DR

This paper classifies 41 types of physical quantities in arbitrary dimensions using Clifford Algebra, introducing wedge reversion as a new symmetry operation to improve classification beyond traditional traits.

Contribution

It introduces wedge reversion as a new symmetry operation, enabling a comprehensive classification of multivectors representing physical quantities in arbitrary dimensions.

Findings

Identifies 41 types of physical quantities in Clifford Algebra

Shows traditional traits like axiality and chirality are insufficient for classification

Demonstrates wedge reversion's role in classification

Abstract

It is shown that there are 41 types of multivectors representing physical quantitites 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, namely, spatial inversion, time reversal, and a third that is introduced here, wedge reversion. It is shown that the traits of axiality and chirality are not good basis for classifying multivectors in arbitrary dimensions, and that introducing wedge reversion would allow for such a classification. Examples of these multivectors from non-relativistic physics are presented.