On page 34 of A. Zee's book QFT in a Nutshell, he states:
I expect you to remember the concept of polarization from your course on electromagnetism. A massive spin 1 particle has three degrees of polarization for the obvious reason that in its rest frame its spin vector can point in three different directions.
- I understand that the spin of a spin-1 particle is a 3-vector, because it is the fundamental representation of $SO(3)$.
- I also know from classical ED that the polarization of light can be quantitatively described using a 3-vector.
But why is this the same? Why is the second implication obvious:
$$ \text{Spin}\,1 \implies \text{Spin} \in \mathbb{R}^3 \implies \text{Polarization} \in \mathbb{R}^3 \, ? $$
