# About spin 3/2 theory ### 1. Spin 3/2 "ONLY" have spin-2 self interaction on S-channel ![](https://i.imgur.com/tsgpIl4.jpg) ![](https://i.imgur.com/jiw7QDy.jpg) ### 2.Spin 3/2 couple gravity with others * #### use dimension analysis: * get the #pole * get the internal paricle helicity * on the s-pole: ![](https://i.imgur.com/Iy1OLRp.jpg) * so we need at least ONE pole of other channel: ![](https://i.imgur.com/zzPAkb8.jpg) ![](https://i.imgur.com/VDHwsvx.jpg) ### 3.Spin 3/2 theory : Labels and Coupling constants * #### 3/2 is non-abelian: ![](https://i.imgur.com/etdPx0V.jpg) * #### Others if 3/2 is non-abelian: ![](https://i.imgur.com/KMvKnJJ.jpg) [推導在這裡](https://drive.google.com/file/d/1OrW9Pm3C7vwfRUPafj71Eq-FRNB3vTy6/view?usp=sharing) * if s=0: ![](https://i.imgur.com/YittYQg.png) * if not: ![](https://i.imgur.com/s5mtAoH.jpg) ![](https://i.imgur.com/Ke4Mvdo.png) ![](https://i.imgur.com/5mmg5no.jpg) ![](https://i.imgur.com/zhRUehZ.jpg) ![](https://i.imgur.com/v0TaVAX.png) ![](https://i.imgur.com/mXEFCl7.jpg) ![](https://i.imgur.com/oGTgrtK.png) ![](https://i.imgur.com/0S2UYyH.jpg)