Derive the completeness relations ∑s=1,2 u^(s)(p) u̅^(s)(p)=p+m,
∑s=1,2 v^(s)(p) v̅^(

Question

Derive the completeness relations      ∑s=1,2 u^(s)(p) u̅^(s)(p)=p+m, 
     ∑s=1,2 v^(s)(p) v̅^(

Accepted Answer

Step 1: Understand the notation and context.
The spinors ( u^{(s)}(p) ) and ( v^{(s)}(p) ) are s

Derive the completeness relations $$ \begin{aligned} & \sum_{s=1,2} u^{(s)}(p) \bar{u}^{(s)}(p)=p+m, \\ & \sum_{s=1,2} v^{(s)}(p) \bar{v}^{(s)}(p)=p-m . \end{aligned} $$ These $4 \times 4$ matrix relations are used extensively in the evaluation of Feynman diagrams (see Chapter 6).