fermions - Legal values of spin-1/2 field can take: $mathbb{R}$, $mathbb{C}$, $mathbb{H}$, .. (Grassmann)?

For the spin-1/2 fermion field $\psi$, we may choose it to be a spinor which needs to be

• Grassmann variable

but can also be

• complex $\mathbb{C}$ Grassmann. (Dirac or Weyl spinor/fermion)


• We can ask: Can be in real $\mathbb{R}$ Grassmann. (Majorana or Majorana-Weyl spinor/fermion)

What are the legal values of spin-1 field can take? real $\mathbb{R}$, complex $\mathbb{C}$, quaternion $\mathbb{H}$, .. (Grassmann)? (p.s. I remember S Adler tries to construct quaternion QFT -- is this related to the quaternion field.)