What happens to the fermion spin when I move around it in a full circle

Question

I would like to understand the actual meaning of the description of a fermion as a spinor. I have a background in QFT and understand the calculations, but there is a leap to the actual experiment which I am not I able to visualise.

Suppose I have a fermion standing still (ignore the technical details, I just want to understand what in principle QFT tells us about the spin transformation).

I now measure the spin along the z-axis and find that it is up. Now I make a full circle around it, coming back to the initial position, without touching the particle.

Will I still measure a spin up along the z direction?

Is it because my rotation relative to the spring is actually two circle and not one? Doe it means that if I make only half rotation, to the antipodal point I will measure the sign difference?

If this is indeed the case, then I think that the whole "spin is getting a minus sign after a full rotation" is a bit misleading. I understand that when "rotating the fermion 360 degrees" rather then moving myself around it does flip its rotation, but this is less troubling for me.

Answer 1

My confusion arised from the fact that the phase of the state gets a minus sign, not thr expectations value of the spin.

Trivial, but I must throw some of the responsibility on people that visualising the fermion phase with a drawing of a ball, with a plus or minus sign, while talking on its spin.