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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Branch cuts in two-point function

The propagator of a QFT is known to have a branch cut as a function of the (complex) external momentum. The branch point (as done by, say, Peskin & Schroeder in eqn.7.19 section 7.1) is ...
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Higgs mass and the hierarchy problem

I was wondering what is the opinion about importance of the hierarchy problem in the hep community? I'm still a student and I don't really understand, why there is so much attention around this issue. ...
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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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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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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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48 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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122 views

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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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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Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
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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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262 views

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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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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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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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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51 views

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 the connection between Conformal Field Theory and Renormalization group in QFT?

As I know, the fundamental concept of QFT is Renormalization Group and RG flow. It is defined by making 2 steps: We introduce cutting-off and then integrating over "fast" fields $\widetilde{\phi}$, ...
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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, ...
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Renormalizing QED with on-shell fermions

When renormalizing QED, we calculate the 1 loop correction to the fermion-fermion-photon vertex using the diagram, $\hskip2in$ When doing the calculation we typically let the photon go off-shell ...
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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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51 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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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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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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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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What is the difference between pole and running mass?

For example, when we meassure Higgs boson mass to be 125 GeV, do we think about renormalized or pole mass? Should the mass of the Higgs change if it is produced at higher energies?
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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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Effective operator in four-fermion interaction

In one book, I have got the following lines which I found myself unable to understand what is effective operator? The paragraph is given below: The weak interaction describes nuclear beta decay, ...
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Experimental determination of $\Lambda_{QCD}$

I have a question about $\Lambda_{QCD}$, the energy scale at which there is a transition from the regime of perturbative QCD to quark confinement. How it is measured experimentally?
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Why holographic renormalization?

Why is there a need to perform holographic renormalization for the normal $AdS_5\times S^5$/CFT$_4$ correspondence if the brane theory is conformal? Since the flow along the AdS direction $r$ is ...
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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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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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Why regularization?

In quantum field theory when dealing with divergent integrals, particularly in calculating corrections to scattering amplitudes, what is often done to render the integrals convergent is to add a ...
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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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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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What exactly is regularization in QFT?

The question. Does there exist a mathematicaly precise, commonly accepted definition of the term "regularization procedure" in perturbative quantum field theory? If so, what is it? Motivation and ...
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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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Which values of the Riemann zeta funtion at negative arguments come up in physics?

For my bachelor's thesis, I am investigating Divergent Series. Apart from the mathematical theory behind them (which I find fascinating), I am also interested in their applications in physics. ...
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Charge renormalization point in massive abelian gauge theory

Let's assume massless QED. The Ward identities hold. Through this identity we determine the finite part of the counterterm when fix the value of electric charge to be the experimentally observed one: ...
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How to expand free energy of Heisenberg spin chain?

In Dasgupta & Ma's 1979 paper "Low-temperature properties of the random Heisenberg antiferromagnetic chain", they give the free energy of a few interacting Heisenberg spins on a chain. I can't ...