Clifford Algebras and Spinors (London Mathematical Society Lecture Note Series, Series Number 239) by Pertti Lounesto (PDF)

Description

In this book, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. A new classification of spinors is introduced, one based on bilinear covariants of physical observables. This reveals a new class of spinors, residing between the Weyl, Majorana and Dirac spinors. Scalar products of spinors are classified by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy’s integral formula is generalised to higher dimensions.

User’s Reviews

Editorial Reviews: Review ‘The author gives a consice but thorough introduction to spinors and Clifford algebras … A very recommendable book for everyone interested in this field.’ Monatshefte für Mathematik’This is a remarkable book … the book is perfectly presented.’ European Mathematical Society’Different parts of the book can be used for different purposes.’ European Mathematical Society’… can be warmly recommended to students or researchers interested in the topic.’ EMS Newsletter Book Description An introduction to Clifford algebras and spinors for physicists and mathematicians.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

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