electronic reprint ISSN: 2053-2733 journals.iucr.org/a Wedge reversion antisymmetry and 41 types of physical quantities in arbitrary dimensions Venkatraman Gopalan Acta Cryst. (2020). A76, 318–327 IUCr Journals CRYSTALLOGRAPHY JOURNALS ONLINE Copyright c International Union of Crystallography Author(s) of this article may load this reprint on their own web site or institutional repository provided that this cover page is retained. Republication of this article or its storage in electronic databases other than as specified above is not permitted without prior permission in writing from the IUCr. For further information see https://journals.iucr.org/services/authorrights.html Acta Cryst. (2020). A76, 318–327 Venkatraman Gopalan · Wedge reversion antisymmetry research papers Wedge reversion antisymmetry and 41 types of physical quantities in arbitrary dimensions ISSN 2053-2733 Venkatraman Gopalan* Department of Materials Science and Engineering, Department of Physics, and Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802, USA. *Correspondence e-mail:
[email protected] Received 18 October 2019 Accepted 16 February 2020 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 Edited by S. J. L. Billinge, Columbia University, symmetry operations on a general multivector: spatial inversion, 1, time- USA reversal, 10, and a third that is introduced here, namely wedge reversion, 1†.Itis shown that the traits of ‘axiality’ and ‘chirality’ are not good bases for extending Keywords: multivectors; wedge reversion antisymmetry; Clifford algebra. the classification of multivectors into arbitrary dimensions, and that introducing 1† would allow for such a classification.