Spin is not related to the 3D real space wavefunction transformation.
What is the fundamental origin of spins?
Or, what is the extra dimension?
Don’t we live actually in a 3+1 D space instead of 3D?
“Rotation symmetry” in 3+1 D: Lorentz symmetry.
Wavefunctions with spins are actually the basis for the representation of rotation transformations in 3+1D.
Fundamentally, spins arises from the special relativity.
Quantum mechanics + relativity –> Relativistic quantum mechanics, or more precisely, quantum field theory (in relativity, a force has to be carried by a field to avoid instantaneous interaction.)
— Page 37, general angular momentum and spin
— 2007-08 PHY5410 Quantum Mechanics II
— Professor Renbao Liu
2011.02.16 Wednesday ACHK