Geometry of spin: Clifford algebraic approach

Abstract

Spin is a fundamental degree of freedom of matter and radiation. In quantum theory, spin is represented by Pauli matrices. Then the various algebraic properties of Pauli matrices are studied as properties of matrix algebra. What has been shown in this article is that Pauli matrices are a representation of Clifford algebra of spin and hence all the properties of Pauli matrices follow from the underlying algebra. Clifford algebraic approach provides a geometrical and hence intuitive way to understand quantum theory of spin, and is a natural formalism to study spin. Clifford algebraic formalism has lot of applications in every field where spin plays an important role.