The real Clifford (or, geometric) algebra is a convenient tool to handle geometric objects, and study relations among them. In this talk I draw attention to spinors, both in space and in spacetime, and advocate the approach, in which they are regarded as elements of the even subalgebra of a real Clifford algebra. With this formalism, I will reexamine the minimal coupling procedure in the Dirac equation, and argue that it leads naturally to a certain non-Abelian generalisation of the electromagnetic gauge potential. [See arXiv:1908.04590 for more details.]