reading this sentence from wikipedia:
The Pauli matrices (after multiplication by i to make them anti-Hermitian) also generate transformations in the sense of Lie algebras: the matrices iσ1, iσ2, iσ3 form a basis for the real Lie algebra, which exponentiates to the special unitary group SU(2). The algebra generated by the three matrices σ1, σ2, σ3 is isomorphic to the Clifford algebra R^3, and the (unital associative) algebra generated by iσ1, iσ2, iσ3 is effectively identical (isomorphic) to that of quaternions.
Does it mean that:
Pauli matrices are just Quaternions, and
Dirac Equation is simply quaternion-version of Schroedinger equation? (just because some phase rotates in 4D not just 2D space)
I know this is more-or-less the same question as here or here, but the answer was too theoretical. I would like somebody to tell me this in layman's terms.
I'm quite familiar with quaternions from programming 3D engines in games where are used to represent 3D rotations. But what Pauli matrices represent was always a mystery to me. So if somebody make this connection (without using to much obscure language) it would make the things more clear and didactic from start.
