# Tagged Questions

Renormalization is an ensemble of techniques which serves to treat the infinities which appear in quantum field theory or statistical mechanics.

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### Structure of Mass Renormalisation

I'm currently working on the renormalisation part in Peskin, Schroeder QFT. There it is stated that non-logarithmic UV divergences give a mass renormalisation and thus are forbidden, e.g. for the ...
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### Divergent diagrams in QED

I was reading about how to choose divergent diagrams in QED by using the concept of Superficial degree of divergence. We have an empirical relation $$D= 4-E_b -\frac{3}{2}E_f$$ where $E_b$ is number ...
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### Is a lagrangian with a background field interaction renormalizable ? If yes, when?

Consider the Lagrangian, $$L = -\partial_{\mu} \chi \partial_{\nu} \chi^{\dagger} - m^2 \chi \chi^{\dagger} + g\chi \chi^{\dagger}\phi,$$ where $\phi$ is a background field and $\chi$ is a complex ...
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### Cutoff-dependent “inverse propagator” for renormalization

In Zee's QFT in a Nutshell, when introducing mass renormalization, he calculates the "inverse propagator" for a $\phi^4$ scalar field theory to order $\lambda^2$ by considering the two diagrams shown: ...
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### Counterterm Lagrangian and Renormalisation?

I am going through the notes on QFT by M. Srednicki (online: http://web.physics.ucsb.edu/~mark/qft.html), and I am having a hard time to understand the "renormalised" Lagrangian. Consider a Klein-...
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### Why would renormalization be necessary without divergent integrals? [duplicate]

Weinberg uses the LSZ reduction formula to introduce field renormalization,and on page 441, he says: As this discussion should make clear: the renormalization of masses and fields has nothing to ...
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### Will Anderson's Poor Man's Scaling loose its effect when band width is small?

The s-d interaction Hamiltonian is as fellows $H_I=Js.S$, J is the coupling strength. We focus on the antiferromagnetic case, where $J>0$. According Anderson's poor man's scaling, the ...
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### Resummation of large logarithms in effective field theory

I am trying to learn about the ideas of large-logarithms in effective field theory from a set of notes. However the following paragraph is confusing me: This doesn't seem quite right to me. Surely ...
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### What is the problem with quantizing GR in the Effective Field Theory approach?

In the modern view due to Wilson, the cut-off $\Lambda$ is an intrinsic property of a theory and renormalization just means that the theory is invariant under scale transformations below $\Lambda$. ...
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### Running coupling, effective potential and the stability of vacuum

Consider the potential $$V(\phi)=\frac{1}{2}\mu^2\phi^2+\lambda\phi^4$$ where $\phi=\phi(t,\textbf{x})$ is a real scalar field. Let, $\mu^2<0$ and $\lambda>0$ then the potential is bounded from ...
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### Questions about the beta function in QFT

When someone defines $\beta(g)=\mu\frac{dg}{d\mu},\quad (1)$ he is implicitly assuming that the result of the rhs of this equation can be written only in terms of $g$ instead of $\mu$, which is not ...
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### Are the bare parameters of a renormalizable field theory infinitesimal or infinite?

I think this should be an easy question. Several sources I've read say that the bare parameters in a quantum field theory are "infinite" so that the renormalized values are "finite". However, in ...
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### Difference between DMRG (density matrix renomalization group) and MPS (matrix product states)?

I am learning DMRG recently. I noticed there are many papers both in the DMRG approach and MPS (such as variational matrix product state (VMPS) by F.Verstraete and J.I.Cirac) approach. In my eyes, ...
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### Why is quantising gravity so difficult? [duplicate]

Since gravity is so similar with the Yang-Mills theory, the Christoffel connection is the gauge potential, the Riemann curvature is the field strength, then why is quantising gravity so difficult when ...
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### What should I think of a diverging beta function (in Renormalisation Group flow)?

I have written a set of RG flow equations using Functional Renormalisation Group methods. I am looking at the flow of a well known problem with an additional original coupling. I did not do anything ...
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### Meaning of counterterms and quantum corrections

When one talks about the “classical Lagrangian” of a field, does one mean the tree-level Lagrangian with physical masses and physical couplings? If yes, does it therefore mean that the bare Lagrangian ...
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### Top quark mass $m_t$ at energy scales $\mu < m_t$?

Edit - Maybe formulated differently: Does it make sense to talk about the top mass at energies below $m_t$, although in all processes the corresponding energy scale is above $m_t$, because of the rest ...
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### Dimensional Regularization for $\phi 4$ theory

When using dimensional Regularization for $\phi 4$ theory to calculate the running of the mass, why there is no quadratic divergence as expected? For details, cf https://workspace.imperial.ac.uk/...
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### What is “the scale at which a theory is defined”?

I'm trying to learn the renormalization group, but I am confused about renormalization schemes. The general idea of RG is that physical predictions are independent of "the scale at which a theory is ...
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### How do people go about looking for asymptotic safety in quantum gravity?

Do we have (proposed?) methods to look for fixed points in the renormlaization group flow of the Einstein-Hilbert action? My understanding of the RG is still somewhat sketchy at this point and I am ...
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### Numerically extracting free energy in renormalization procedure

I have some doubts about how to apply real space renormalization numerically. I understand the theoretical concept, and how we require $Z'=Z$, being $Z'$ the partition function of the renormalized ...
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### Mass of an imaginative stable top quark at low energies? [duplicate]

Masses are not fixed quantities, but change with energy because of the renormalization group running. These can be calculated in a given renormalization scheme, for example, the MS scheme: Imagine ...
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### What are the six quark mass values when extrapolated to Planck energy?

Let us assume that the standard model is correct up to Planck mass. (Yes, I know, this is a big assumption.) If we continue the running of quark masses with energy (due to renormalization), what are ...
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### On the c-theorem

I have been reading a few papers on CFT and AdS/CFT regarding the c-theorem and I have a few questions regarding c-theorems: a) Why is it that the c-theorem is usually considered for only unitary ...
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### Continuous renormalisation

In Quantum Field Theory and the Standard Model, M.D. Schwartz talks about how Wilsonian renormalisation relates to continuous renormalisation. He states that continuous renormalisation looks a ...
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### W and Z boson masses' running neglected?

Since the Lagrangian mass term of $W$ boson involves the bare coupling $g$, it cannot be the measured mass. Then the measured mass will "run" with momentum transferred. But everywhere I look the "...
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### Renormalization group resummation

I'm having trouble in understeanding a mathematical feature of RG, namely how it provides a way to resum the perturbation series and how that's defined mathematically. From a conceptual point of view ...
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### How can we calculate pion decay constant in Chiral Perturbation Theory ?

Above diagram is an one-loop contribution to the Pion decay constant $f_\pi$. For example in this paper (Eq.7) they have written down the pion decay constant to one loop, but the calculation is not ...
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### Understanding the $\phi^4$ phase diagram

I'm having trouble making sense of this phase diagram. The model is a $V(\phi)=g_2 \phi^2+g_4\phi^4$ scalar field theory. Here's what I think I understand: the capital letters represent different ...
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### S-matrix element for forward scattering and amputed green function

I'm studying dispersion relations applied as alternative method to perturbation theory from Weinberg's book (Vol.1) Let's consider the forward scattering in the lab frame of a massless boson of any ...
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### Regularization of the Casimir effect

For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have ...
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### multi-dimensional renormalization group flow?

Suppose you have $\lambda \phi^3$ theory, and that you renormalize the 2 and 3 point one-particle irreducible graphs, $\Pi_R(p^2)$ and $\Gamma_R(p_1,p_2,p_3)$, by Taylor expanding about $p=\mu_0$ for ...
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### Can the terms in the microscopic model with nonzero conformal spin generate some new term(s) under RG (renormalization group) flow?

As in the book Bosonization and Strongly Correlated Systems at page 66, it says that "We see that the original perturbation with nonzero conformal spin generates the perturbation with zero conformal ...
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### A question about the implication of UV divergence in QFT

I have a basic question about the logic of renormalization in quantum field theory (QFT). We met the ultraviolet (UV) divergence in loop corrections. The standard argument is, our current field theory ...
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### Renormalization Group Invariance of Scattering Amplitude

How can one show that the scattering amplitude is renormalization group invariant using the fact that the bare Green's function $G_0^{(n)}$ is renormalization group invariant? We have: \$(1) \quad ...
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### Am I understanding correctly the argument that leads to the need for field and mass renormalization?

I'm studying Quantum Field Theory from Weinberg's book, and I'm to the point where he introduces the concept of renormalization. I'd like to know if I'm getting the point that Weinberg makes when ...
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### Physical meaning of Ward Identity and computing vertex functions

Following the derivation of Ward Identity by Weinberg book, you get it in the form $$(l-k)_\mu S'(k)\Gamma^\mu(k,l)S'(l) = i S'(l) - iS'(k)$$ Can anyone explain the physical meaning of this ...
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### Can I use Pauli-Villars and dimensional regularization together?

There are at least two ways to compute the electron-self energy. You can use Pauli-Villars or dimensional regularization, for example. On Weinberg's book, it's chosen the first method, while on my ...