When one applies block spin scheme on Ising model, what's the value for block spin? If we set the average value for spin in a block, it should not be ±1 anymore. But if so, is the transfer matrix is still two dimensional?
Or in other words:
The renormalization group is a systematic theoretical framework and a set of elegant (and often effective) mathematical techniques to build effective field theories, valid at large scales, by smoothing out irrelevant fluctuations at smaller scales.
But does the...
I'm reading about extensions of standard model and this pops up frequently but it's not very clear. I understand it's a region in parameters space so renormalization group naturally becomes relevant and that's about it for my understanding. I can't connect any of this to the beta function of the...
Years ago after reading Ch. 12 of Peskin and Schroeder (and the analogous discussion in Zee), I thought I fully understood the modern Wilsonian view of renormalization, and how it explains why non-renormalizable field theories still have meaning/predictive power at energies well below the...
In his paper Quantum Field Theory: renormalization and the renormalization group Zinn-Justin states:
Low energy physics does not depend on all the details of the microscopic model because some RG has an IR fixed point or at least a low dimension fixed surface. Of course at this stage the next...
There are several reasons given in the literature, why UV infinities arise in QFT in the first place. My problem is putting them together, i.e. understand how they are related to each other.
So... UV divergences arise and thus we need to renormalize, because:
We have infinite number of...
I am aware of only two fields where the renormalization (sub)group ideas can be systematically and
unambiguously applied: particle physics and equilibrium critical behaviour.
1.- Are there any others?
2.- What are these ideas used for in fluid mechanics?
3.- When cosmologists speak about...
I'm currently studying the Landau-Wilson model for critical phenomena (Statistical Mechanics, Kerson Huang) where the renormalization group is a central object. In the end, the calculations lead to a set of coupled differential equations that describe the (metaphorical) evolution of the...
Given a Yukawa coupling as a function of scale and a vev, how can I compute the corresponding pole mas?
Understandably most paper explain how from a measured pole mass one can compute the running mass, for example, Eq. 19 here. However I want to compute the pole mass from the running mass. In...
Does it make sense to talk about the top mass at energies below mt, although in all processes the corresponding energy scale is above mt because of the rest mass energy of the top quark?
Using an effective field theory approach, the top quark decouples at energies below the top quark mass and...
The top and Higgs mass determination arose the old discussion about electroweak vacuum metastablity. There is an interesting fact that with available data the universe places in the edge of stable and meta-stable zone tends to be inside the meta-stable region. This conclusion confirms up to...
On page 164-165 of srednicki's printed version (chapter 27) on other renormalization schemes, he arrives at the equation $$m_{ph}^{2} = m^2 \left [1 \left ( +\frac{5}{12}\alpha(ln \frac{\mu^2}{m^2}) +c' \right ) + O(\alpha^2)\right]$$
But after taking a log and dividing by 2 he arrives at...
The problem statement.
When an exercises say " the interaction in a QFT has dimensions Δ" , what does it mean?, it means the field or the Lagrangian has this mass dimension?
In this exercise I'm trying to find the classical beta function (β-function) for the assciated couling.
Hi there,
I have a question about the rest mass of an electron. As we all know, the charge of an electron is a function of the energy at which the system is probed. When defining the charge, we typically use as our reference scale the charge measured in Thompson scattering at the orders of...