Cambridge University Press Cambridge Clifford Algebras: An Introduction - LMS Student Text

Explore the fundamental principles of Clifford algebras with this comprehensive introduction from Cambridge University Press. Part of the London Mathematical Society Student Texts series, this volume provides a clear path into algebraic structures built from quadratic spaces. Clifford algebras serve as natural generalizations of complex numbers and quaternions, making them essential for advanced mathematical study. This text covers their vital role in proving the Atiyah-Singer index theorem and their ability to provide double covers of classical groups through spin groups. It also explains how these algebras generalize the Hilbert transform. Beyond pure mathematics, this book connects algebraic theory to physical reality. You will learn how Clifford algebras set the stage for Maxwell's equations in electromagnetic theory, explain the spin of elementary particles, and support the Dirac equation. This straightforward guide is designed to build the necessary algebraic background for students and researchers working in mathematics and physics.