Well I noticed that with what I have, I can rewrite the fields in the way most online sources I’ve seen have them (with e.g the field phi being a sum of a annihilation operator of a certain type and a creation operator of a different type). These new operators end up being linear combinations of...
I'm self-studying QFT and attempting exercise 2.2 on Peskin & Schroeder. First off, I'm a bit confused on the logic the authors use in the quantization process. They first expand the fields in terms of these ##a_{\vec{p}},a_{\vec{p}}^\dagger## operators which, if I understand correctly, is...
I'm trying to make sense of the derivation of the Klein-Gordon propagator in Peskin and Schroeder using contour integration. It seems the main step in the argument is that ## e^{-i p^0(x^0-y^0)} ## tends to zero (in the ##r\rightarrow\infty## limit) along a semicircular contour below (resp...
I'm self-studying field theory and trying to solidify my understanding of index manipulations. So I've been told that there is a general rule: " If the index is lowered on the 'denominator' then it's a raised index". My question is whether this is just a rule or something that can make sense...