Algebraic and Quantum Mechanical Approach to Spinors

Clifford algebras and quantum mechanics are closely associated to each other. We are familiar with some popular terms, such as algebra, light polarization, and quantum spin. Dirac spinors, Majorana spinors, and Weyl spinors are discussed in particular as subspaces of Clifford algebras with some remarkable algebraic features. Furthermore, we are interested in demonstrating how the quantum spin state and classical polarization of light waves can be derived from one another along with the Bloch sphere and Poincare sphere representations.