Equation (7.25)(adsbygoogle = window.adsbygoogle || []).push({});

[tex](\displaystyle{\not}p - m)(1 - {\left. {\frac{{d\Sigma }}{{d\displaystyle{\not}p}}} \right|_{\displaystyle{\not}p = m}}) + O({(\displaystyle{\not}p - m)^2})[/tex]

Formally it looks like a Taylor expansion of [itex]\displaystyle{\not}p-m_{0}-\Sigma(\displaystyle{\not}p)[/itex]. However it involves a differentiation of a matrix, and what's worse is, he lets [itex]\displaystyle{\not}p=m[/itex], which is impossible because [itex]\displaystyle{\not}p[/itex] is always off-diagonal(peskin uses weyl representaion), while m is diagonal.

The best I can make of this [itex]\displaystyle{\not}p=m[/itex] is that this is just a formal replacement, but then Taylor expansion loses its meaning of "polynomial approximation around the neighbourhood of a point", since [itex]\displaystyle{\not}p[/itex] can never really approach m.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Meaning of Peskin equation (7.25)

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**