Clifford Algebras and Spinors

Rating:
Summary: The best introduction to Clifford algebras.
Review: A very clear and comprehensive introduction to a somewhat esoteric subject; essential for anyone in theoretical physics (especially field theory). It is possible to teach yourself the subject from this book alone--a rare feature in mathematics texts. Bravo!

Rating:
Summary: For the Physicist - Not the Mathematician
Review: Clifford algebras make geometry and its applications to advanced physics incredibly simple, and this book is one of the best that I have read on this topic and on spinors. Readers outside physics should also study this book, if necessary with the help of a consultant or tutor to translate into more or less ordinary English, because most fields of science or industry are in need of tremendous simplification. Lounesto's approach is algebraic, as is Okubo's (see my review of his book) and Chisholm's (likewise), and Cambridge University Press as usual is at the head of the field in publishing the deepest and yet most simple topics. Spinors (the word comes from spin plus the ending -ors) describe spin in quantum theory, and Lounesto has the most detailed division of the types of spinors that I have seen in a book together with their physical applications. Weyl and Majorana spinors describe the neutrino (of the weak force, although the former only describe massless neutrinos), flagpole spinors appear to describe the strong nuclear force/interaction and appear to be related to quark confinement, Dirac spinors describe the electron (Weyl and Majorana spinors, unlike Dirac spinors, are singular with a light-like pole/current). Penrose flags (see my reviews of Roger Penrose's books) are related to Weyl and Majorana spinors. Penrose has an interesting theory of twistors which is well reviewed in some of the popular science books.

Rating:
Summary: Lounesto's Clifford Algebras and Spinors
Review: Clifford algebras make geometry and its applications to advanced physics incredibly simple, and this book is one of the best that I have read on this topic and on spinors. Readers outside physics should also study this book, if necessary with the help of a consultant or tutor to translate into more or less ordinary English, because most fields of science or industry are in need of tremendous simplification. Lounesto's approach is algebraic, as is Okubo's (see my review of his book) and Chisholm's (likewise), and Cambridge University Press as usual is at the head of the field in publishing the deepest and yet most simple topics. Spinors (the word comes from spin plus the ending -ors) describe spin in quantum theory, and Lounesto has the most detailed division of the types of spinors that I have seen in a book together with their physical applications. Weyl and Majorana spinors describe the neutrino (of the weak force, although the former only describe massless neutrinos), flagpole spinors appear to describe the strong nuclear force/interaction and appear to be related to quark confinement, Dirac spinors describe the electron (Weyl and Majorana spinors, unlike Dirac spinors, are singular with a light-like pole/current). Penrose flags (see my reviews of Roger Penrose's books) are related to Weyl and Majorana spinors. Penrose has an interesting theory of twistors which is well reviewed in some of the popular science books.

Rating:
Summary: For the Physicist - Not the Mathematician
Review: Lounesto's book is replete with geometric and physical applications. The treatment is informal and non-rigorous and appears to have been designed with developing intuition in the reader. The text starts slowly working through many examples of particular Clifford algebras of interest and their relevence to physical problems. Towards the end Lounesto investigates general Clifford algebras and their associated spin groups as well as some specialized topics.

This is a good introductory text but fails to give the reader a firm mathematical basis of the material. Most striking is the almost total lack of proofs of any kind - the author is content merely to state the most important results but seldom leaves the reader with any mathematical justification. As such it is really a primer and the student of Clifford algebras must after working through the material move beyond to a rigorous algebraic text.