Hi all, I am troubled by the flag and flagpole analogy for two-spinors and would like some clarification. Please refer to the post by Hans de Vries. https://www.physicsforums.com/showthread.php?t=239191 Am I right to say that the usage of spin rotation operators (eg exp(-i([itex]\phi[/itex]/2)σ(x)), which is a [itex]\phi[/itex] degrees rotation in the 3D space about the positive x axis would affect the phase factor of the spinor? spinor s is given by s = s*exp(-i([itex]\alpha[/itex]/2)) (cos([itex]\vartheta[/itex]/2))exp(-i([itex]\phi[/itex]/2)), sin([itex]\vartheta[/itex]/2))exp(i([itex]\phi[/itex]/2))) (column vector here) note, alpha, theta and phi represent angle of the flag about the flagpole, angle downwards from the z-axis and angle from the x-axis. phi here is not the same as the arbitrary phi for the spin rotation operator. My question is whether it is true that when the spin rotation operator is used, it affects the term exp(-i([itex]\alpha[/itex]/2) in a way such that a rotation of 360 degrees makes the spinor negative and thus a rotation of 720 degrees is needed for the spinor to return to its original state. Ie, when the flagpole rotates, the flag is also rotating but while the flagpole has a period of 360 degrees(like a usual vector in 3D), the flag has a period of 720 degrees. I mean is this the only way to see how spin rotation operators affect the spinor? (in other words the state of electron) This is because I can't see directly how rotation operators affect the phase factor other than this way. Please enlighten me. Thank you.