Quaternionic treatment of Dirac equation — 1 articles found.

In Praise of Quaternions

C. R. Math. Rep. Acad. Sci. Canada Vol. 35 (4) 2013, pp. 121–136
Vol.35 (4) 2013
Joachim Lambek Details
(Received: 2013-03-04 , Revised: 2013-06-25 )
(Received: 2013-03-04 , Revised: 2013-06-25 )

Joachim Lambek, Department of Mathematics and Statistics, McGill University, Montreal, PQ Canada; e-mail: lambek@math.mcgill.ca

Abstract/Résumé:

This is a survey of some of the applications of quaternions to physics in the 20th century. In the first half century, an elegant presentation of Maxwell’s equations and special relativity was achieved with the help of biquaternions, that is, quaternions with complex coefficients. However, a quaternionic derivation of Dirac’s celebrated equation of the electron depended on the observation that all $4\times 4$ real matrices can be generated by quaternions and their duals.

On examine quelques applications des quaternions à la physique du vingtième siècle. La première moitiè du siècle avait vu une présen-tation élégante des équations de Maxwell et de la relativité spéciale par les quaternions avec des coefficients complexes. Cependant, une dérivation de l’équation célèbre de Dirac dépendait sur l’observation que toutes les matrices $4\times 4$ réelles peuvent être generées par les représentations régulières des quaternions.

Keywords: Classification of elementary particles, Quaternionic treatment of Dirac equation, Three temporal dimensions

AMS Subject Classification: 16A40

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