Analysis of Dirac Systems and Computational Algebra

Preface Background Material Computational Algebraic Analysis for Systems of Linear Constant Coefficients Differential Equations The Cauchy-Fueter Systems and its Variations Special First Order Systems in Clifford Analysis Some First Order Linear Operators in Physics Open Problems and Avenues for Further Research References Index

From the reviews:

"The book presents a uniform treatment of some fundamental differential equations for physics. Maxwell and Dirac equations are particular examples that fall into this study. The authors concentrate on systems of linear partial differential equations with constatn coefficients n the Clifford algebra setting...The material is presented in a very accessible format...The book ends with a list of open problems that pertain to the topic." --- Internationale Mathematische Nachrichtén, Nr. 201

"The first 138 pages of this book are a good introduction to algebraic analysis (in the sense of Sato), and some computational aspects, in the setting of quaternionic analysis. But the core of the book is the study of different important systems of partial differential equations in the setting of Clifford analysis...The last chapter states some open problems and avenues of further research. A rich list of references, an alphabetic index and a list of notation close the volume. Well-written and with many explicit results, the book is interesting and is addressed to Ph.D. students and researchers interested in this field." --- Revue Roumaine de Mathématiques Pures et Appliquées

"Altogether the book is a pioneering, and quite successful, attempt to apply computational and algebraic techniques to several branches of hypercomplex analysis ... The book provides a very different way to look at some important questions which arise when one tries to develop multi-dimensional theories."(MATHEMATICAL REVIEWS)