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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How do the renormalization enter the actual amplitude calculation in QFT?

I have studied QFT from Peskin and Schroeder and from a few other books and lectures and I think I understand the procedure of renormalizing various parameters in the Lagrangian like mass, coupling ...
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Mass and wave function renormalization In chiral perturbation theory

Before I put forward my actual question, I think it will be useful to set the context in a clear way and that involves my understanding of a few very basic things of Chiral Perturbation Theory. ...
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Is interaction a relevant perturbation for 1d Anderson localization of fermions?

Disorder is a relevant perturbation in 1d, which drives the system to Anderson localization. My question is if I am already at the Anderson localization fixed point, how to analyze the scaling ...
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renormalization subtraction point, scaling

When we use minimal subtraction scheme, for instance, we have a dependence of coupling on a scale $\mu$. Using the $\beta$ function, we can observe the behavior of the coupling at different scale ...
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QED renormalization: mass and dirac field

Why the mass renormalization $Z_m$ and the field renormalization $Z_\psi$ in QED (MS-renormalized) does not contribute to the beta function computation? From Ward identity, I know that $Z_A=Z_e^{-1}$, ...
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Renormalization: in particular “ A hint of renormalization ” by Bertrand Delamotte [duplicate]

Per http://arxiv.org/pdf/hep-th/0212049.pdf His equation (22) and his statement " We show in Appendix B that, reciprocally, this choice is always possible if (15) is fulfilled. " As one will see ...
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Clarification on Use of Counterterms in Renormalized Perturbation Theory

In renormalized perturbation theory, it's unclear to me how exactly we add the necessary counter-terms. Do we: Draw all possible diagrams, including the diagrams of the counter-terms to some order ...
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In QFT how do you write down the most general interactions?

This past year I took a QFT class and I now feel comfortable solving scattering problems, but I am still a bit perplexed by how physicists write down a Lagrangian in the first place. In particular, ...
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Doubts with basic renormalization

When we renormalize to obtain the physical mass, the $\Lambda$ dependence of the physical mass is removed by introducing the counterterms in the Lagrangian. So whether we put ...
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“ A hint of renormalization ” by Bertrand Delamotte [closed]

Renormalization: in particular " A hint of renormalization " by Bertrand Delamotte Has anyone read and understand well this article ? I have begun reading it and has cleared up a few basic questions ...
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Statistical field theories on topological defects

Systems like superconductors and superfluids are often treated by specifying some phenomenological mean field theory where the free energy is given as a functional of some order parameter field. Given ...
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Physical explanations for renormalization

Some related questions on Renormalization: Why is renormalization even necessary? My understanding is that the supposed problem is that the sums of certain amplitudes end up being infinite. But ...
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Why can we set mass to zero in Yukawa RGE derivation?

In problem 12.1 from Peskin&Schroeder's book I have to derive the beta functions in massless Yukawa theory. What's the justification for setting mass to zero and what's the difference between ...
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78 views

Field theory in four dimensions

I was reading Schwartz's book on QFT. In chapter 14.5 at p.267, while speaking about path integral he says: [...] the path integral (and field theories more generally) is only known to exist (i.e. ...
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51 views

Assumptions in the LSZ reduction formula

In Srednicki, Chapter 5, it is said that the LSZ reduction formula holds only under the assumptions $$ \langle 0|\phi(x)|0\rangle =0 \qquad\text{and} \qquad \langle k|\phi(x)|0\rangle =e^{-ikx}$$ I ...
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Why is QCD hard to solve if I know the beta functions?

Why is it still hard to solve QCD if we know the beta functions of the coupling? Aren't only the loops causing problems? And am I not able to write every possible interaction exact at tree-level with ...
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63 views

Amputated Green's function in the LSZ formula

From Schwartz's QFT textbook, under Ch.18, Mass renormalization, Schwartz introduces a new LSZ formula with renormalized Green's function. He states that the new LSZ formula for QED, with pole mass ...
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43 views

What is primitive divergence?

As in the title, what is primitive divergence? How is it distinguished from normal divergence? As a followup, what is a primitive divergent graph in a theory? Some simple examples?
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What exactly is Weinberg's power counting theorem?

The massive gravity propagator goes like $\sim \frac{p^2}{m^4}$ at high energies and in this case we cannot apply Weinberg's standard power counting arguments. I have read something like that ...
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What is meant by “the superpotential is not renormalized”?

Reading about supersymmetry I often read the phrase because of the non-renormalization theorems the superpotential is not renormalized. I would like someone to be more explicit on what is ...
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Why does regularization work in this Bessel function integral?

I encountered some days before an integral representation for a modified Bessel function and should differentiate it. But in this representation : $$K(\omega,a)=\int_0^{\infty} \frac{ds}{s} ...
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Renormalization Using Momentum Cut-off Regularization, What Are The Subtraction Schemes Used?

In most of the books on QFT, the author talks about various methods of regularization but in the end chooses the dimensional regularization and MS-bar scheme when discussing the final renormalization, ...
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How sketch the renormalization group flows in the $(\lambda, e^2)$ plan for scalar QED?

I have obtained beta functions of renormalization group for scalar QED: $$ \beta (e) = \frac{e^3}{48 \pi^2} $$ $$ \beta(\lambda) = \frac{1}{24\pi^2}(5\lambda^2 - 18e^2\lambda + 54 e^4) $$ which give ...
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Are gauge theories always renormalizable?

Speaking of quantum field theories. Is one of the following implications correct? gauge theory (gauge invariant) => renormalizable renormalizable => gauge theory (gauge invariant) If yes do you ...
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Renormalization of Auxiliary Fields

I have the following non-linear sigma model (the base space $\mathcal{M}$ is Euclidean): $$ \mathcal{L}=\dfrac{1}{2\alpha}\int_{\mathcal{M}}\mathrm{d}^2\sigma\ \partial^2X^{\mu}\partial^2X_{\mu} $$ ...
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Infinite bare quantities and dressed quantities confusion

I'm getting very confused. Taking the example of the mass of the Z-boson. Constructing the GWS model using gauge symmetry breaking one finds a lagrangian which is a function of the Z-boson mass: ...
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Doubts in understanding the role if quantum corrections in the Hierarchy Problem

Trying to understand the Hierarchy problem many questions come to my mind that I am unable to answer due probably to my poor understanding of renormalization. The basic set up of the hierarchy ...
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What is the procedure to follow if I want to renormalize a given operator $\cal{O}$ or a given coupling?

Consider QED. I know that the renormalization constant of the mass can be obtained from considering the electron propagator, regularizing it and renormalizing it. I know that from this process we can ...
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What is renormalization? [closed]

What is renormalization? I would want a rough description before I go and work on it properly (I did a course on QFT and on SM (which was 3rd course in the series) but skipped the 2nd course which ...
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50 views

Can we just replace the finite part of $Z_m$ in a renormalization scheme at leading order

Suppose that we have to determine the finite part of $Z_m$ how it differs from common schemes, but we are free to choose the other renormalization constants in QCD (at Leading order). Could we make ...
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Can we change the point form $\not p = m$ to $\not p = 0$ in on-shell renormalization scheme condition?

In the on-shell scheme, in QCD, one can impose the counterterms action to vanish the part of 1PI diagrams on external lines. The on-shell condition can be written as follows: \begin{equation} {\left. ...
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Relation between Wilson approach to renormalization group and 'standard' RG

While studying renormalization and the renonormalization group i felt that there wasn't any completely satisfying physical explanation that would justify those methods and the perfect results they ...
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What is meant by the phrase “this operator does not renormalize this other operator”, and how can understand it using diagrammatic arguments?

I am trying to understand some sentences in a paper. In section two the following theory of a (complex) massless scalar coupled to a $U(1)$ gauge boson is introduced ...
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EFT and Renormalizability

Was trying to understand renormalizability in EFT. This is a little confusing especially the part of the misnomer. Can someone please explain this? Text taken from Wikipedia: "However, in an ...
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Deriving solution of the Renormalization Group Equation

I am trying to follow Matthew Schwartz's renormalization group lectures (pdf or see Chapter 23 of QFT and the SM by Matthew Schwartz), but I am having trouble with Eq. (book 23.31/pdf 29). I ...
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What does mathematical equivalence means here?

On Motls blog, http://motls.blogspot.com/2012/06/on-importance-of-conformal-field.html, while I was trying to understand what dimensional transmutation means, he said: I said that by omitting the ...
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Can you take the cutoff to infinity at a conformal fixed point?

A conformal fixed point is defined by $$\beta(g)=0$$ We hence know that couplings, masses and dimensions of operators do not flow in the effective Lagrangian when we change the renormalization ...
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Epstein-Glaser causal perturbation theory

Why does causal perturbation theory in the sense of Epstein Glaser fall under algebraic QFT rather than heuristic QFT in renormalization?
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Scalar QED perturbation theory [closed]

Where can I find material about scalar QED? Renormalization, scattering matrix, perturbation theory, etc...
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Is gauge invariance essential to a theory be renormalizable?

Let's consider a model of New Physics in which all operator have dimension smaller than four, but which breaks explicitly $SU(2)_L$ gauge symmetry. Is this model necessarily renormalizable? ...
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Non-pertubative renormalization and correctness of a theory

Even if I start to understand why perturbative renormalization is necessary, I'm not exactly sure why non perturbative renormalization is. After asking the question to several theorists, what I think ...
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Is the exact form of the Higgs potential known?

Usually the Higgs potential is given as $$ \frac{1}{2}\mu^2\phi^2 - \frac{1}{4}\lambda^2\phi^4 $$ but I never quite understood if this just serves to give us an idea of how symmetry breaking works, or ...
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Why doesn't a renormalizable $\phi^4$ theory have odd diagrams?

I've been reading Zee's QFT textbook and trying to follow some lecture notes online whenever I can't grasp something. I really don't understand one thing regarding the renormalization of theories, ...
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Around fixed point of renormalization group

In the general formulation of renormalization group in "statistical mechanics" by P.K.Pathria, each point in parameter space is represented by a vector $\vec{K}$ and the transformed vector would be ...
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What is precisely the energy scale of a process?

Coupling constants run with the energy scale $\mu$. But what is exactly this energy scale. My question is, if I have a physical process, how do I compute $\mu$?
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Why IR divergences cancel by cross sections of next-to-leading diagrams?

I was reading QFT & Standard Model by Schwartz, Chapter 20 which is about IR divergences. He says that IR divergences only cancel cross sections for processes involving different initial or ...
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Why don't we have logarithms or exponentials of the fields in the Lagrangians?

All tbe Lagrangian densities I have seen have always been polynomials of the fields. Is this a coincidence or is there a reason forbid, say, Lagrangians with logarithms or exponentials of the fields?
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Temperature and Renormalization Scale in QFT

A particle physicist told me that everything in Peskin & Schroder is at zero temperature, and once you consider finite-$T$ QFT, things become more complicated. Meanwhile, I sometimes see people ...
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Why is it correct to estimate divergences by the cutoff in QFT?

Let's say we have a linear divergence in a quantum field theory. The way to deal with this infinite quantum correction is to go through the whole process of renormalization. However, quite often, ...
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Anyonic braiding statistics from density matrix renormalization group (DMRG) simulations

How does the ground state energy of the system change when we braid two anyons? Can the braiding of anyons be simulated with a computational method such as the density matrix renormalization group, ...