# Peskin 3.82

1. Apr 24, 2010

### sunkesheng

peskins introduction to QFT [3.82],do not know what he had done to the underline

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2. Apr 24, 2010

### ansgar

write out the components of each entry in the matrices

3. Apr 24, 2010

### sunkesheng

i see ,but why the \singma[\nu]\sigma[\lambta] in the first row can be write to that in the second row,

4. Apr 24, 2010

### ansgar

what properties of the sigma can u think of?

5. Apr 24, 2010

### sunkesheng

many thanks .it is my fault,i dont express my question clearly,so
sigma is the 2*2 pauli matrix ,but subscript of the front two sigma matrixs in the first row is \beta ,in the second it changes to \delta,that is what i puzzled.

6. Apr 24, 2010

### ansgar

just write out every dirac index and massage it

7. Apr 24, 2010

### sunkesheng

get it ,there is a change which is important and very simple ,and it is until now that i realized it :
\sigma^{\mu}_{\alpha\beta}=\sigma^{\mu}^{T}_{\beta\alpha}
thanks a lot!

8. Apr 25, 2010

### ansgar

ah great, I was about to do this all for myself so that I could pin-point exactly what is going on ;)

It "always" work to write out the Dirac indices

One thing I dont like is that Peskin uses greek letter for Dirac index sometimes.. like here, very annoying and confusing

9. May 7, 2012

### oopsitbroke

For posterity, here's a step-by-step derivation of line 1 to line 2 of eqn. 3.82 for Peskin & Schroeder QFT.

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