Main issue: What are the legal and possible values of the quantum field can take?

Clarify by examples:

(1) For example, for the spin-0 Klein Gordon field $\phi$,
we may choose it to be:

- real $\mathbb{R}$.
- complex $\mathbb{C}$.

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

but can also be

- complex $\mathbb{C}$. (
**Dirac or Weyl spinor/fermion**)
- We can ask: Can it be in real $\mathbb{R}$? (
**Majorana or Majorana-Weyl spinor/fermion**)

(3) For the spin-1/ boson field $A_\mu$,
we may choose it to be a vector which needs to be

(3) How about the spin-3/2 fermion field $\psi_\mu$?

- can it be in real $\mathbb{R}$, complex $\mathbb{C}$, quaternion $\mathbb{H}$, ..?

This post imported from StackExchange Physics at 2020-11-24 18:31 (UTC), posted by SE-user annie marie heart