Clifford numbers and spinors. Ed. by E. Folke Bolinder, Pertti Lounesto
type: Item
instance of: scholarly article
title: Clifford numbers and spinors. Ed. by E. Folke Bolinder, Pertti Lounesto
zbMATH Open document ID: 0823.15028
published in: Fundamental Theories of Physics
publication date: 1995-07-16T00:00:00Z
review text: This book is useful for students as an introductory course on Clifford algebras and will be of value to those interested in the history of mathematics. The book contains a facsimile reproduction of Riesz's notes of a set of lectures delivered at the University of Maryland in 1957-58, which has not been published to date. The seminal material (arranged in four chapters), which contributed greatly to the start of modern research on Clifford algebras, is supplemented in this volume by notes on electromagnetism which Riesz dictated to E. F. Bolinder in 1959 and which were indented to be a fifth chapter of the Riesz lecture notes. Present-day researchers would benefit from the counter-examples which Riesz gives to common misconceptions. Riesz shows that all elements of \(\text{Spin}_ + (1,3)\) are not exponentials \(e^ B\) of bivectors \(B \in \Lambda^ 2 \mathbb{R}^{1,3}\), and that all elements of \(\text{Spin}_ + (2,2)\) cannot be written in the form \(\pm e^ B\) where \(B \in \Lambda^ 2 \mathbb{R}^{2,2}\) [cf. \textit{G. M. Dixon}: Division algebras: octonions, quaternions, complex numbers and the algebraic design of physics (1994; Zbl 0807.15024)], page 13, and \textit{C. Doran}: Geometric algebra and its applications to mathematical physics, Thesis, Univ. Cambridge (1994), page 41].
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 15-01
zbMATH DE Number: 774555
zbMATH Keywords: introductory textbook
zbMATH Keywords: spinors
zbMATH Keywords: Clifford algebras
zbMATH Keywords: counter-examples
MaRDI profile type: Publication
author: Marcel Riesz
description: scientific article; zbMATH DE number 774555