Understanding Normalization in Spin Sum: Peskin vs. Kaku and Zee's Approach"

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nklohit
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In Peskin's textbook, he uses the spin sum as [tex]\sum u\bar{u} = \gamma^{\mu}p_{\mu} +m[/tex] ;
on the other hand, in Kaku's book and in Zee's book, they use [tex]\sum u\bar{u} = \dfrac{\gamma^{\mu} p_{\mu} + m}{2m}[/tex] . But why aren't there any diffferent in the differential cross
section formula ?
 
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The normalization condition should not affect any physical result.