Hi everyone! I have a few questions regarding renormalization in QFT.(adsbygoogle = window.adsbygoogle || []).push({});

1. In Peskin chapter 10, he renormalizes [tex]\phi^4[/tex] theory using the renormalization conditions in equation (10.19), which basically say that the propagator has a pole at [tex]p^2=m^2[/tex] and that the 4-point interaction is exact for [tex]s=4m^2[/tex]. These are reasonable assumptions (I think). However, in equation (12.30) of chapter 12, he introduces a different set of renormalization conditions defined at a spacelike momentum. I.e. the propagator is defined at [tex]p^2=-M^2[/tex] and the four point function is defined at [tex]s=t=u=-M^2[/tex]. These are unphysical values, why are these renormalization conditions valid (or reasonable)? Why not use [tex]+M^2[/tex] and physically accessible conditions?

2. In chapter 12 section 4 he describes the renormalization of local operators. Is it correct to define a local operator as one that is roughly of the form [tex]\phi(x)^n[/tex]? In the diagrams for the Greens function with a local operator on page 431, the diagrams being summed have different numbers of legs! (Similar to page 601-603) I don't quite understand what's going on here and why these diagrams with different in/out states can be summed together.

3. In chapter 11, p. 355, why is it acceptable to use the "tadpole diagram = 0" renormalization condition in place of the usual one for the propagator? How is this equivalent to the propagator condition?

Thanks very much,

Flip

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

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

# Renormalization Conditions

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