{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:00:49Z","timestamp":1760230849682,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,13]],"date-time":"2022-08-13T00:00:00Z","timestamp":1660348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In practical engineering, the use of Pauli algebra can provide a computational advantage, transforming conventional vector algebra to straightforward matrix manipulations. In this work, the Pauli matrices in cylindrical and spherical coordinates are reported for the first time and their use for representing a three-dimensional vector is discussed. This method leads to a unified representation for 3D multivectors with Pauli algebra. A significant advantage is that this approach provides a representation independent of the coordinate system, which does not exist in the conventional vector perspective. Additionally, the Pauli matrix representations of the nabla operator in the different coordinate systems are derived and discussed. Finally, an example on the radiation from a dipole is given to illustrate the advantages of the methodology.<\/jats:p>","DOI":"10.3390\/sym14081684","type":"journal-article","created":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T23:44:03Z","timestamp":1660607043000},"page":"1684","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Unified Representation of 3D Multivectors with Pauli Algebra in Rectangular, Cylindrical and Spherical Coordinate Systems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8534-0220","authenticated-orcid":false,"given":"Ben","family":"Minnaert","sequence":"first","affiliation":[{"name":"Cosys-Lab, Departement of Electromechanics, University of Antwerp, 2020 Antwerp, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0595-2310","authenticated-orcid":false,"given":"Giuseppina","family":"Monti","sequence":"additional","affiliation":[{"name":"Departement of Engineering for Innovation, University of Salento, 73100 Lecce, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3655-0296","authenticated-orcid":false,"given":"Mauro","family":"Mongiardo","sequence":"additional","affiliation":[{"name":"Departement of Engineering, University of Perugia,  06123 Perugia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,13]]},"reference":[{"key":"ref_1","unstructured":"Maxwell, J.C. 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