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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Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section ...
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About equivalence of two ways of “derivation” of Standard model

Two ways of SM derivation I know two methods of SM lagrangian "derivation". The first one, which I will call as Weinberg way, is based on approaches of SM as theory with spontaneusly broken ...
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The divergence in QCD Series— How many are they, and what do they mean?

I am referring to this question, and especially this answer. In addition, QCD has - like all field theories - only an asymptotic perturbation series, which means that the series itself will ...
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Ultraviolet behaviour in dimensional regularization

In dimensional regularization, we introduce an arbitrary energy scale $\mu$. Naively, it plays the role of another parameter of the theory that needs to be fixed experimentally, but actually it is not ...
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Scalar field divergent mass correction interpretation question (hierarchy problem)

Simple power counting tells you that a scalar field coupled to some fermions at one-loop picks up a correction to the mass of the order $\Lambda^2$. Based on this people say things like "it's natural ...
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How to handle the infrared divergence of massless $\phi^4$ in scattering

For massless $\phi^4$ theory, if exterior momentums are going to zero, then this diagram will be $$\int \frac{dk^4}{k^4}$$ will suffer from infrared divergence. Because the infrared divergence, ...
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Why is gravity so hard to unify with the other 3 fundamental forces?

Electricity and magnetism was unified in the 19th century, and unification of electromagnetism with the weak force followed suit, bringing into play the electroweak force. I've been told that ...
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Momentum Space Renormalization of $\phi ^6 $ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d $ for the energy functional: $$ f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2 $$ where $\ d$ is the dimension ...
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Renormalization Group and Ising with d=1 and D=1

I have a question about the results of RG on Ising model. I know it's possible to obtain two couple of relations $K'(K)$, $q(K')$ $K(K')$, $q(K)$ between the coupling costants. My problem arise ...
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How do I apply a renormalization technique to estimate the fractal dimension of a diffusion limited aggregate?

Diffusion Limited Aggregation (DLA) is an interesting phenomena observed in nature and discussed here. From a theoretical view point, it'd be nice to know about the fractal dimension of a DLA formed ...
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Integral derivation [closed]

Somebody know how to derive this integral? \begin{equation} \int \frac{d^Ds}{(2\pi)^D} \frac{s_\mu (p-s)_\nu}{s^2(p-s)^2} = \frac{i}{(4\pi)^2} \left(\frac{4\pi ...
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What is the $D_{x^2-y^2}$ symmetry/channel/instabilitied referred to with regards to super-conductivity?

I have been reading various articles on Renormalization group where they compute the flow of some parameter which becomes increasingly attractive and then say that parameter is responsible for Cooper ...
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Relation between renormalisation matrix and anomalous dimension

I need an relation between the renormalization constant matrix and the anamalous dimension matrix. Now I found the following derivation \begin{equation} \begin{split} \gamma (a_\mu) &= ...
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39 views

Does quantum chromodynamics imply continuous space? [duplicate]

I am thinking it does. That's because a pillar of quantum chromodynamics is renormalization, which is itself due to the assumption that electrons are point particles (having no extent). A point ...
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173 views

Do perturbative renormalization groups help one understand when perturbation theory can be used in general?

If, as I asked in this question, a relevant operator in a renormalization group transformation can't be used in a perturbative expansion since it becomes large as the transformations are applied, does ...
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373 views

Does the Standard Model have a Landau pole?

I have seen the statement that the Standard Model has a Landau pole, or at least it its believed that it does at $\sim 10^{34}$ GeV. Has this actually been proven (at least in perturbation theory, as ...
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19 views

How to interpret “smooth momentum space slicing” in renormalization group analysis?

Ref: [John B. Kogut, Rev. Mod. Phys. 51, 659 (1979), An introduction to lattice gauge theory and spin systems]. More precisely, please refer to Page 703 within the section of renormalization group ...
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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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Is the stability matrix of a linearised RG flow always diagonalisable?

This is a follow up on "Why are the eigenvalues of a linearized RG transformation real?". My question is simple: Is there some physical (or mathematical) reason for the stability matrix of ...
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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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Any textbook about non-renormalizability of gravity?

I have learned general relativity in a graduate-level. My knowledge about QFT is very rudimentary. But, I need to learn about non-renormalizability of gravity. I have these questions. Is there any ...
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A functional average calculation confusion within Gaussian planar model's RG

I am trying to follow some detailed calculation in a famous paper [John, B. Kogut, Rev. Mod. Phys. 51, 659 (1979), An introduction to lattice gauge theory and spin systems]. More precisely, please ...
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59 views

How to choose the proper loop correction?

I review my QFT lecture notes and I am having hard times to figure out the significance of Ward identity in vacuum polarization. In class, we calculated one loop correction stated as $$ ...
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CP-violation in weak and strong sectors

There is a possible CP-violating term in the strong sector of the standard model proportional to $\theta_\text{QCD}$. In the absence of this term, the strong interactions are CP-invariant. In the ...
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How Ward Identity indicate vacuum polarization correction?

In Peskin & Schroeder Chapter 7.5 Renormalization of The Electric Charge, they mention that vacuum polarization correction is $$ iM= (-ie)^2(-1)\int_{}{}\frac{d^4k} ...
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Aren't $\phi^4$ composite operators?

I have this trouble with terminology. I wonder why authors introduce the concept of composite operators after they've already talked about eg phi four theory, it phi cubed. Aren't these operators ...
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Why does not the bare interaction potential appear in the Bogoliubov theory?

They use some effective potential defined by the s-wave scattering length, but not the bare atom-atom interaction $V(r)$. Why? It is standard practice in second quantization to use the bare ...
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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 ...
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Do particles with exactly zero energy exist?

In my understanding, in Newtonian mechanics if something has no mass it cannot be said to "exist" since it cannot possibly have energy or momentum and thus cannot participate in interactions or be ...
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How are scale of renormalization and scale of symmetry breaking related?

If symmetry breaking, e.g. with a potential $V=-\mu^2\phi^2 + \lambda \phi^4 $ occurs at a certain energy scale, and I now evolve to another scale via the Callan-Symanzik equations, does that change ...
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Typical Momentum Invariants of a General 3-Point Function for Renormalization Conditions

According to Peskin, p.414, at the bottom, as part of calculating the $\beta$ functions of a theory, we need to fix the counter terms by setting the "typical invariants" built from the external leg ...
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Rigorous Proof of General Relativity's Non-renormalizability?

The answer to this question and the comments on it implies that general relativity has not been rigorously shown to be non-renormalizable for all loop diagrams -- only shown for two loops. However, ...
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Is there a maximum number of fixed points that a QFT can have?

I was wondering: is there a maximum number of (trivial and non-trivial) fixed points that a QFT can have (as a function of the space-time dimension and field content in the QFT)?
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Calculation of Beta Functions in Yukawa Theory

I am trying to calculate the $\beta$ functions of the massless pseudoscalar Yukawa theory, following Peskin & Schroeder, chapter 12.2. The Lagrangian is $$\mathcal{L}=\frac{1}{2}(\partial_\mu ...
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Two math methods apply the same loop integral lead different results! Why?

I tried to adopt the cut-off regulator to calculate a simple one-loop Feynman diagram in $\phi^4$-theory with two different math tricks. But in the end, I got two different results and was wondering ...
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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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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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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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Logarithmic discretization in Anderson´s model

Is there some motivation for the construction of Ladder operator that compound the recursive halmitonian of the Anderson model for numerical renormalization contained is this paper?
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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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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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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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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. ...