A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics. The book under review, itself an Introduction, is another entry in the excellent Garling hits Clifford algebras proper and proceeds with the. : Clifford Algebras: An Introduction (London Mathematical Society Student Texts) () by D. J. H. Garling and a great selection of.
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London Mathematical Society Student Texts: An Introduction Series Number Description Clifford algebras, built up from quadratic spaces, have applications inrtoduction many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah-Singer index theorem, to provide double covers spin groups of the classical groups and to generalize the Hilbert transform.
They also have their place in physics, setting the scene for Maxwell’s equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background – including multilinear algebra, quadratic spaces and finite-dimensional real algebras – easily accessible to research students and final-year undergraduates.
The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts.
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London Mathematical Society Student Texts: Clifford Algebras: An Introduction Series Number 78
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Clifford Algebras: An Introduction – D. J. H. Garling – Google Books
The Laplacian on a Riemannian Manifold: Volume 1 Ibrahim Assem. Table of contents Introduction; Part I.
Groups and vector spaces; 2. Algebras, representations and modules; 3. Multilinear algebra; Part II. Quadratic Forms and Clifford Algebras: Classifying Clifford algebras; 7. Representing Clifford algebras; 8. Some applications to physics; Representations of Spind and SO d ; Some suggestions for further reading; Bibliography; Glossary; Index. Of all the books written on the subject, Garling’s is by garlling way the most compact and concise Math students will find it ideal for quickly covering a range of algebraic properties, and physicists will find it a very handy source of reference for a variety of material.
The book is written in a concise way and provides a precises introduction to the old and new developments concerning Clifford’s ideas. It can be used by either students or researchers in aglebras or physics who want to master this important subject.
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