Clifford, or Geometric, Algebra

Abstract In this chapter, the so-called geometric algebras, or Clifford algebras, are introduced, with special attention to the universal Clifford algebras. As well as providing the standard definition of a Clifford algebra via the so-called Clifford mapping, this chapter presents an explicit construction of the universal Clifford algebra associated with a quadratic space as a quotient of the tensor algebra. Clifford algebras are also presented in the context of Grassmann algebras. In addition, the prominent features of Clifford algebras are presented and creation operators and annihilation operators are introduced. All the topics presented in this chapter are illustrated with a number of different, enlightening examples.