P. Lounesto - Böcker

This volume contains a facsimile reproduction of Marcel Riesz's notes of a set of lectures he delivered at the University of Maryland, College Park, between October 1957 and January 1958, which has not been formally published to date. This material (arranged in four chapters), which contributed greatly to the start of modern research on Clifford algebras, is supplemented in this book by notes which Riesz dictated to E. Folke Bolinder in the following year and which were intended to be a fifth chapter of the Riesz lecture notes. In addition, Riesz's work on Clifford algebra is put into an historical perspective in a separate review by P. Lounesto. As well as providing an introduction to Clifford algebra, this volume should be of value to those interested in the history of mathematics.

This text introduces mathematicians and physicists to a crossing point of algebra, physics, differential geometry and complex analysis. It follows the French tradition of Cartan, Chevalley and Crumeyrolle and summarizes Crumeyrolle's own work on exterior algebra and spinor structures. The depth and breadth of Crumeyrolle's research interests and influence in the field is investigated in a number of articles. Of interest to physicists is the modern presentation of Crumeyrolle's approach to Weyl spinors and to his spinoriality groups, which are formulated with spinor operators of Kustaanheimo and Hestenes. The Dirac equation and Dirac operator are studied both from the complex analytic and differential geometric points of view, in the modern sense of Ryan and Trautman. This book is intended for mathematicians and mathematical physicists whose research involves algebra, quantum mechanics and differential geometry.

This volume contains a facsimile reproduction of Marcel Riesz's notes of a set of lectures he delivered at the University of Maryland, College Park, between October 1957 and January 1958, which has not been formally published to date. This seminal material (arranged in four chapters), which contributed greatly to the start of modern research on Clifford algebras, is supplemented in this book by notes which Riesz dictated to E. Folke Bolinder in the following year and which were intended to be a fifth chapter of the Riesz lecture notes. In addition, Riesz's work on Clifford algebra is put into an historical perspective in a separate review by P. Lounesto. As well as providing an introduction to Clifford algebra, this volume will be of value to those interested in the history of mathematics.