# Nature of Spin in QFT

If the orbital angular momentum of an electron in an atomic orbital is associated with (generated by) an asymmetry in the orbital wave function, is it also the case that the intrinsic spin of a free electron (as one specific example) in QFT is associated with an asymmetry in the coherent excitation pattern of the electron matter field/EM field constituting the electron? Or, is intrinsic spin more fundamental, perhaps relating to the fact that the underlying matter field is a spinor field.

• What do you mean by "an asymmetry in the coherent excitation pattern of the electron matter field/EM field constituting the electron"? – my2cts Feb 11 at 21:29
• For example, the two conjugate phased nodes of an individual p-orbital. – CSnowden Feb 13 at 3:42

The spin of the particle is determined by the dimension of the representation that it assumes under the double covering group $$SL(2,\mathbb{C})$$ of the Lorentz group $$SO(1,3)$$. For example, spin 1/2 particles live in the fundamental (or spin-1/2) representation of $$SL(2, \mathbb{C})$$. These come in either left handed reps (1/2,0) or in right handed reps (0,1/2), both of which are spin 1/2 representations.
• There's a bit of terminological confusion in this answer: The unitary representations of the Poincaré group are all infinite-dimensional and not the finite-dimensional representations denoted by a pair of half-integers $(s_1,s_2)$ you talk about later. – ACuriousMind Feb 12 at 19:29