For the spin-1/ boson field Aμ, we may choose it to be a vector which needs to be
real R usually for photon field. The field strength F=dA is also real. Same for the nonabelian case F=dA+A2 is also real.
but can A be complex C?
but can A be quaternion H?
What are the legal values of spin-1 field can take? real R, complex C, quaternion H , ..? And what may be the QFT like in these cases?
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