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