All Questions
Tagged with renormalization perturbation-theory
96
questions
2
votes
1
answer
114
views
What does it mean to "resum" the large logarithms?
I am struggling to understand the concept of resummation of large logarithms in QFT; from what I learnt so far the problem relies on the fact that if a full theory defined in the UV contains much ...
- 477
1
vote
2
answers
105
views
Why is Perturbative expansion of gravity in terms of $GE^2$?
From General Relativity by Weinberg p.797 edited by Hawking & Israel:
This is to be used to generate a perturbation series in powers of $GE^2$ or $G/r^2$ (where $E$ and $r$ are an energy and a ...
- 23
1
vote
0
answers
55
views
$Z_1=Z_2$ and its relation to vertex renormalization in QED
I have been working on the full renormalization of scalar QED with self-interactions, following the steps of Schwartz’s treatment on spinor QED (Chap 19). I have 3 main questions regarding this:
Need ...
- 162
0
votes
0
answers
25
views
How to study regularity of a Green's function when solving field equations perturbatively?
Preliminaries
Consider a nonlinear differential operator $\mathcal{O}$ acting on a field $\phi$, with source $\rho$
$$\mathcal{O}(\phi)=\rho$$
Let's say the charge density is small, so we can define $\...
- 4,827
5
votes
1
answer
205
views
Wilsonian RG in QFT: what is the difference between renormalized and bare couplings?
I want to understand the relation between the Wilsonian RG and the usual QFT RG approach. Several questions have been asked, such as this and many others, yet I don't find a conceptual answer to what ...
- 1,989
2
votes
1
answer
79
views
Why are the corrections to the effective Lagrangian (Wilsonian renormalization) given by connected diagrams only?
This question will fully refer to the presentation ref. 1, from which I'll take the numbering. Since it involves also diagrams and it appears as a fairly basic question about Wilsonian renormalization,...
- 1,989
2
votes
1
answer
105
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How does the on-shell (OS) scheme work if we assume mass to be zero?
When calculating the self-energy correction of a massless quark up to one loop, I get
$$i\Sigma(p)=i\frac{\alpha_s}{4\pi}C_F/\!\!\!{p}\left[\frac{1}{\varepsilon_{\text{UV}}}-\gamma+\ln(4\pi)+1+\ln(\...
- 172
2
votes
1
answer
88
views
How is dimensionality of $S$ preserved term by term in a perturbative expansion?
In a schematic notation, the scattering matrix element $$\langle p_{out}|S|p_{in}\rangle := 1 + i (2 \pi)^4 \delta^4(p_{in} -p_{out}) M$$ between an incoming state with momentum $|p_{in}\rangle$ and ...
- 307
1
vote
1
answer
119
views
Contradiction in energy scales with regard to running coupling and observables
Here is the contradiction, which I arrive at.
Renormalization group (RG) eqs. are basically a statement that observables (cross-section or Green's function) don't depend on the arbitrary ...
- 837
4
votes
1
answer
196
views
Renormalization in $\lambda\phi^4$-theory: Why renormalize at one-loop instead of renormalizing at order of the coupling constant $\lambda$?
I am reading about one-loop renormalization in the $\lambda\phi^4$-theory. Instead of doing renormalization at order $\lambda$, why are we interested in renormalization at one-loop which contains both ...
- 11.8k
2
votes
0
answers
55
views
Renormalization conditions and proper vertices at tree level
I'm trying to understand a statement of my teacher of TQFT: he said that when expanding the effective action in terms of proper vertices, we can choose a new theory with only tree diagrams in order to ...
- 167
1
vote
0
answers
63
views
One-loop renormalization of $\phi^4$ theory in Cheng and Li
In Gauge Theory of Elementary particle Physics by Cheng and Li, They manipulate the self-energy 1PI vertex as
I am quite confused how one gets (2.20), what type of expansion is this?
- 460
0
votes
1
answer
109
views
Dimensional Analysis and Power Counting in $R$ and $R^2$ Gravity Perturbation Expansions
In the context of $R$ gravity, the perturbation expansion appears as:
$$
S=\int \left( \partial \tilde{h} \partial \tilde{h} + X \tilde{h} \partial \tilde{h} \partial \tilde{h} + ... \right) d^4 x
$$
...
- 1,548
1
vote
0
answers
41
views
Perturbative calculation of hierarchy problem
I've been trying to understand the origin of the hierarchy problem for the Higgs mass but I've tied myself into some pretty nasty knots and I'm hoping someone can shed some light on this.
So as I see ...
- 233
5
votes
1
answer
391
views
Why does square of Planck length come as coupling constant when quantizing gravity in 3+1D?
In Birrell and Davies, the author says in the Introduction that
If the gravitational field is treated as a small perturbation, and attempts are made to quantize it along the lines of quantum ...
- 1,931