This manual introduces the mathematical subject of Clifford Algebras, authored by D. J. H. Garling and published by Cambridge University Press. It is designed for research students and final-year undergraduates seeking a straightforward introduction to this topic. The book builds upon concepts from multilinear algebra and quadratic spaces, presenting Clifford algebras as natural generalizations of complex numbers and quaternions. It aims to equip readers with Clifford algebras as a working tool, applicable in various mathematical and physical contexts, including proofs of the Atiyah-Singer index theorem, spin groups, and generalizations of the Hilbert transform, as well as applications in electromagnetic theory and elementary particle physics.
This English-language resource, spanning 200 pages and published on June 30, 2011, provides a comprehensive overview of Clifford Algebras. It covers essential algebraic background and explores their significant applications in both pure mathematics and theoretical physics. The manual is structured to make its foundational concepts accessible, guiding readers through the material to understand the utility and application of Clifford algebras. Its purpose is to serve as an educational tool, fostering a deep understanding of this advanced mathematical structure and its relevance across diverse scientific disciplines.
Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the AtiyahñSinger 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 ñ including multilinear algebra, quadratic spaces and finite-dimensional real algebras ñ 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.
Author: Garling, D. J. H.
Publisher: Cambridge University Press
Illustration: N
Language: ENG
Title: Clifford Algebras: An Introduction
Pages: 00200 (Encrypted PDF)
On Sale: 2011-06-30
SKU-13/ISBN: 9781107096387
Category: Mathematics : Algebra - Abstract
Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the AtiyahñSinger 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 ñ including multilinear algebra, quadratic spaces and finite-dimensional real algebras ñ 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.
Author: Garling, D. J. H.
Publisher: Cambridge University Press
Illustration: N
Language: ENG
Title: Clifford Algebras: An Introduction
Pages: 00200 (Encrypted PDF)
On Sale: 2011-06-30
SKU-13/ISBN: 9781107096387
Category: Mathematics : Algebra - Abstract
