system
Given the following post, respond as if you're commenting on Reddit:
human
What is the origin of spin, from the perspective of quantum field theory?
gpt
Spin arises directly from considering quantum mechanics with rotational symmetry, even without introducing field theory. In any quantum theory with a symmetry, you can arrange all states in irreducible projective unitary* representations of the mathematical group describing that symmetry. For rotations, these representations correspond to states which carry spin. Adding special relativity enlarges the symmetry group, introducing chirality and the fact that states carry a mass (and zero-mass particles have helicity instead of spin). These representations are naturally associated with/defined to be "particles."

Nothing says that you *have* to have particles with a given spin. But our own universe does take advantage of the ability to have particles with nonzero spin.

Relativistic quantum mechanics does end up leading you to introduce quantum fields and quantum field theory - you make all of the operators in your theory into operator-fields which transform in some (not necessarily unitary) representation of the Lorentz group. One usually matches fields with a certain representation with the particles which they create when acting on a state. But these are tools you use to describe spinfull particles, they're not really the "origin" of spin.

\* Or anti-unitary, which usually concerns time-reversal symmetry.