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Power-series expansion in coupling/Planck constant

Feynman diagram techniques are inherently perturbative. Diagramatically, in a theory like scalar $\phi^3$ or QED with a photon and an electron where you have one vertex, an expansion in the coupling ...
Andrew's user avatar
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2 votes

A question on IR divergence in Peskin-Schroeder chapter 6

Four lines after eq. (6.63), Peskin and Schroeder say explictly: "To gain a better understanding of the divergence, let us evaluate the coefficient of the divergent logarithm, $f_{\rm IR}(q^2)$, ...
Hyperon's user avatar
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1 vote

How do vacuum bubbles "dress" terms in the $S$-matrix numerator?

The factorization between the numerator and denominator is perhaps best appreciated by remembering that an $n$-point function in the Heisenberg picture is $$ \langle \phi^{k_1}\ldots \phi^{k_n}\...
Qmechanic's user avatar
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2 votes
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How do vacuum bubbles "dress" terms in the $S$-matrix numerator?

Your second equation is not the full contribution resulting from the Wick decomposition of the numerator up to order $\lambda$ but only the (physically relevant) tree contribution of order $\lambda$. ...
Hyperon's user avatar
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How do vacuum bubbles "dress" terms in the $S$-matrix numerator?

This is a subtle point, illustrated far better than I can in some books linked below. First, I'll try to sketch the cancellation of the vacuum diagrams - Consider the corrections up to second order: (...
catalogue_number's user avatar
2 votes

Some integrals in QED Renormalisation

Your suspicion is justified. You are indeed missing a crucial approximation not mentioned in your post, turning a simple few-line calculation into an exercise in self-torture. The photon mass $m_\...
Hyperon's user avatar
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1 vote

Some integrals in QED Renormalisation

Your complaint is not entirely justified, the first integrand is just a rational function, for which solution methods can easily be found: integration-rational-functions Although tedious, it can be ...
Jos Bergervoet's user avatar
1 vote
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How can I count diagrams (in this scalar QED example) at a particular order without drawing all the Feynman diagrams?

I believe that the approach you outline in your question is more-or-less all that Schwartz is looking for. In particular, with 8 vertices of the type $A_\mu \phi^* \partial_\mu \phi$ and $4$ external ...
QCD_IS_GOOD's user avatar
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Understand "Quantum effective action" in Weinberg's book "The quantum theory of fields"

This equation has already been demonstrated in Peskin's An Introduction to Quantum Field Theory. In section 11.4, Eq. (11.63) corresponds to Eq. (16.1.17) in Weinberg's book. We can write Peskin's ...
ChungLee's user avatar
1 vote
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Divergences in tree-level diagrams?

More generally in perturbation theory, a connected $n$-point tree-diagram $$(2\pi)^d\delta^d(\sum_{j=1}^np_j)~{\cal M}(p_1,\ldots,p_n)$$ in momentum space $$(p_1,\ldots,p_n)~\in~(\mathbb{R}^d)^n$$ ...
Qmechanic's user avatar
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Why do correlation functions involving composite fields require special analysis?

As already pointed out by @Prahar, the problem of the definition of a composite operator arises already in the free theory. Considering the Lagrangian of a free real scalar field, $$\mathcal{L}[\...
Hyperon's user avatar
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1 vote
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Understanding $W^{(n)}$, $\Gamma^{(n)}$, and $\Sigma$ in Feynman diagrams

The connected $n$-point function $$\langle \phi^{k_1}\ldots \phi^{k_n}\rangle^c_{J=0}~=~\left(\frac{\hbar}{i}\right)^{n-1} W_{c,n}^{k_1\ldots k_n}$$ is the sum of connected Feynman diagrams with $n$ ...
Qmechanic's user avatar
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Difference between renormalizable and super-renormalizable theories

Qmechanic's answer is very good and tackles your main question well. I want to however add an important detail to your first question. Namely, we generally do not just consider $[\lambda]$ when ...
mika's user avatar
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3 votes
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Difference between renormalizable and super-renormalizable theories

It should stressed be that Peskin & Schroeder are here using the old Dyson definitions of renormalizability. For a more general derivation of eq. (10.13), see e.g. this Phys.SE post, which also ...
Qmechanic's user avatar
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