Vector Analysis of Spinors

The geometric algebra of space G3 is derived by extending the real number system to include three mutually anticommuting square roots of +1. The resulting geometric algebra is isomorphic to the algebra of complex 2 ×2 matrices, also known as the Pauli algebra. The so-called spinor algebra of C2, the language of the ubiquitous quantum mechanics, is formulated in terms of the idempotents and nilpotents of the geometric algebra G3, including its beautiful representation on the Riemann sphere.