Clifford numbers and spinors. Ed. by E. Folke Bolinder, Pertti Lounesto
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].
scientific article; zbMATH DE number 774555