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I have been looking at the renormalisation of QED and been using Peskin & Schroeder. I understand (I think) what is going on, but I am slightly confused over 2 issues:

1. In the new feynman rules from the counterterms, the feynman diagrams all have a small circle with a cross in them.....what do these represent? (P&S p332, fig 10.4)

2. why do we need the renormalization conditions? (P&S p331-331 eq 10.40)

Help would be much appreciated!

Thanks