The Spinorial Formalism

It is well-known that the rotation symmetries play a central role in the development of all physics. In this book, the material is presented in a way which sets the scene for the introduction of spinors which are objects that provide the least-dimensional faithful representation for the group Spin(n), the group that is the universal coverage of the group SO(n), the group of rotations in n dimensions. With that goal in mind, much of this book is devoted to studying the Clifford algebra in which lies the algebraic idea of a spinor and the basic elements of differential geometry which enabled us to emphasize the more geometrical origin of spinors. This book, thus, is intended to be self-contained at the level of a graduate student of physics or mathematics. A higher-dimensional generalization of the so-called monogenic multivector functions is also investigated and a solution of the monogenic equation for spinor fields on conformally flat spaces in arbitrary dimension is presented. Finally, the spinorial formalism is used to show that the Dirac equation minimally coupled to an electromagnetic field is separable in spaces that are the direct product of bidimensional spaces.