All Questions
Tagged with renormalization interactions
40
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
5
votes
3
answers
271
views
Triviality of $\phi^4$ theory, is it settled now (2024)?
According to the answer on
question 364576
this should be settled. But after looking for clear statements of the current situation on triviality of $\phi^4$ theory, I'm still not sure, because:
In ...
- 4,913
1
vote
1
answer
99
views
Why is $\frac{1}{2}\delta_Z(\partial_\mu \phi_r)^2 - \frac{1}{2}\delta_m \phi_r^2$ treated together in Feynman diagrams?
From P&S consider the $\phi^4$ bare Lagrangian:
$$\mathcal{L} = \frac12 (\partial_\mu \phi)^2 - \frac12 m_0^2\phi^2 - \frac{\lambda_0}{4!} \phi^4.\tag{p.323}$$
When using renormalized perturbation ...
- 3,350
1
vote
1
answer
79
views
What is screening in Quantum Field Theory and how does it influence the strength of interactions in QCD?
Question is fairly straight to the point. In particular, how does it influence the strength of particle interactions?
1
vote
0
answers
60
views
Beta function of two copies of the same model with interactions
I have a particular model with two couplings, let's call it model A, for which I have the set of beta functions and fixed points. Now I am interested in a model where I have two copies of model A, ...
- 61
2
votes
1
answer
163
views
Is it true that there are no known mathematically rigorous examples of interacting QFTs in 4 dimensions?
An answer to a question
(What physical processes other than scattering are accounted for by QFT? How do they fit into the general formalism?) about quantum field theory asserts
"we don't know ...
- 59.6k
0
votes
1
answer
40
views
Should the sign of Feynman rule factors be the same as the sign in the Lagrangian?
Suppose I have this Lagrangian
$$
L = \frac{1}{2}\partial^\mu\phi\partial_\mu\phi - \frac{1}{2}m^2\phi^2-\frac{g_3}{3!}\phi^3
$$
One of the Feynman rules would be associating a factor $(-ig_3)$ to ...
- 1,783
0
votes
1
answer
223
views
How is it justified to use two different coupling constants for tree-level diagrams and diverging diagrams?
For tree-level amplitude, we're using the finite constant determine using experiments ($\lambda _R$)
For diverging amplitudes, we're using a different constant: $\lambda _R+ C\ln \frac{\Lambda ^2}{s_0}...
- 6,355
-3
votes
1
answer
187
views
Is a running coupling constant a natural consequence in QFT, or is it a consequence of the "dressing-up" of particles?
The running coupling constant ("hold that constant!) is a well known phenomenon in quantum field theory. The constant varies with the energy of the interacting particles. I think this is rather ...
3
votes
1
answer
773
views
Dimensional regularization vs. hard cutoff and their relation to the renormalization scale in 2d vs 4d to find $\beta$ functions
I would like to understand some shortcuts people are using to calculate $\beta$ functions using dim. reg. with mass scale $\mu$ and/or the hard cutoff $\Lambda$. My end goal is to use equation 12.53 ...
- 65
2
votes
0
answers
52
views
Why Lorentzian momentum corresponds to $1/$length?
I'm reading Peskin & Schroeder's QFT, the effective coupling related with QED, is given by (7.96):
\begin{align}
\alpha_{\rm eff}(q^2)=\frac{\alpha}{1-\frac{\alpha}{3\pi}\log \left( \frac{-q^2}{Am^...
- 89
2
votes
1
answer
280
views
Is there a simple explanation of why coupling constants run with $\log(E)$?
The inverse coupling constants run with $\log(E)$, where $E$ is the energy or four-momentum.
Some coupling constants increase, some decrease with $\log(E)$.
Is there a simple argument that explains ...
user85598
6
votes
1
answer
558
views
Why are Yukawa couplings regarded as fundamental constants if their values vary with scale?
Why are Yukawa couplings regarded as fundamental constants if their values vary slowly with the energy scale (distance scale) at which they are measured?
This question is the same as why are quarks ...
- 476
1
vote
1
answer
182
views
Confusion on the renormalizability and the dimension of coupling constant (From Srednicki's book)
I am trying to understand the renormalizability and the dimension of couplings from section 18 of Srednicki's QFT book.
In section 18, it mentions if we can use finitely many new terms (counter-term) ...
- 995
3
votes
1
answer
185
views
Lifetime of a particle at the maxima of an unstable potential
Consider an unstable potential of the form $$V(\phi) = - \lambda \phi^n $$ with $\lambda > 0$ (hence unstable). Now due to quantum fluctuations, a particle at the top is going to roll down. So what ...
- 167