- all can be expressed by unitary 4x4 matrices so they seem to represent kind of rotation in 4D space.
- all can be expressed as 2x2 matrix of complex numbers
- So are Dirac spinors just a subset of quaternions or not?
- Or what is the relation, and what are the distinctions?
- And what are the physical consequences?
I wonder why this questions is not discussed anywhere in relation to Dirac equation, since this is the first question I would have. Since the Schrödinger equation is expressed using complex numbers, and the Dirac equation is its 4D version, I would naturally think first about quaternions as the 4D analog of complex numbers.
This also leads to natural question if physically meaningful Dirac equation can be expressed using quaternions instead of Dirac spinor? Or what physical consequences (like alternative physics) it would lead to?