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# System prepended metadata

title: About spin 3/2 theory

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# 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)






