Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== - Spin = intrinsic angular momentum. In quantum theory “spin” labels how a particle transforms under rotations: mathematically it’s an irreducible representation of the rotation group. For 3D rotations the correct technical groups are SO(3) and its double cover SU(2); half-integer spins come from SU(2)’s double cover structure. Rochester School of Arts & Sciences<ref>{{cite web|title=Rochester School of Arts & Sciences|url=https://www.sas.rochester.edu/pas/assets/pdf/undergraduate/su-2s_double_covering_of_so-3.pdf|publisher=Rochester School of Arts & Sciences|access-date=2025-12-16}}</ref>Wikipedia<ref>{{cite web|title=Wikipedia|url=https://en.wikipedia.org/wiki/Spin_%28physics%29|publisher=en.wikipedia.org|access-date=2025-12-16}}</ref> ===
* Spin-½, spin-1, spin-2: these are the simplest representation labels. A spin-½ object changes sign under a 360° rotation (needs 720° to return), a spin-1 object behaves like a vector (3 components in a massive case; massless photon → two helicities ±1), and a massless spin-2 field (graviton) carries the tensor/quadrupole degrees (helicities ±2). Wikipedia<ref>{{cite web|title=Wikipedia|url=https://en.wikipedia.org/wiki/Spin_%28physics%29|publisher=en.wikipedia.org|access-date=2025-12-16}}</ref>arXiv<ref>{{cite web|title=arXiv|url=https://arxiv.org/html/2403.08637v1|publisher=arxiv.org|access-date=2025-12-16}}</ref>
* Why spin matters for interactions and statistics. Spin determines allowed statistics (fermions vs bosons), how fields couple, and the allowed angular-momentum exchange in scattering; spin-2 fields, crucially, force universal coupling (connected to why a consistent massless spin-2 field gives Einstein’s equations in the classical limit). ScienceDirect<ref>{{cite web|title=ScienceDirect|url=https://www.sciencedirect.com/science/article/abs/pii/S1355219820300836|publisher=sciencedirect.com|access-date=2025-12-16}}</ref>