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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independence of the bare parameters on μ for beta function

So I know re-normalization has bean "beaten to death". I want to understand something a bit specific which might seem trivial. Independence of the bare parameters on $\mu$ and relevance to the beta ...
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Amplitudes in renormalized perturbation theory

This question arose while reading Peskin and Schroeder, specifically, it arose in regards to the sum of diagrams above their Eq. (10.20) on pg. 326. The context is $\phi ^4$ theory and they are using ...
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Nonequilibrium themal QFT

Wick rotation to thermal of QFT in Minkowski space to thermal QFT, which is after this transformation analogue to statistical mechanics, does only describe equilibrium statistical mechanics. On page ...
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Dimensional regularization and the finite part

Let be a dimensional regularized integral $$ \int d^{4-\epsilon}kF(k,m,s)= \frac{2}{\epsilon}+\frac{m^{2}}{3}(\gamma +log(4\pi)-\frac{1}{\epsilon}))$$ then formally if we elmiinate the divergent ...
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Can't find the mass scale; calculation using the modified minimal subtraction scheme and dimensional regularisation

I am taking a course on quantum field theory where there is some confusion regarding the renormalisation scheme we are using (and a corresponding one in my mind). Apparently the lecturer meant MS-bar ...
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Divergence in Supergravity

I'm not familiar with supergravity so here's my question: I've heard in talks that if one finds divergence for five-loop 4-graviton scattering amplitudes in five dimensions this translates to a ...
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Why does renormalization need an unbroken symmetry?

Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ...
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Why do string theory and Hopf algebra renormalization seem to have no intersection?

Hopf algebra appears in recent papers that systematize renormalization of quantum field theory (QFT). For example see Connes' work and citing papers or a paper referenced here on PSE: R. E. ...
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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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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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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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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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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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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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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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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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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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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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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 ...
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Dimensional Regularization of the Higgs Mass Correction

I've found plenty of blog posts and papers where the authors claim that the Higgs mass divergence (usually presented with a momentum cutoff) doesn't show up under dimensional regularization. ...
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Does a momentum-independent interaction not renormalize mass?

I recently had to calculate the effective mass to second-order in a momentum-independent interaction in a Fermi liquid, and I found that it was the same as the bare mass. What's more, the first-order ...
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Virtual particles and the scaling effect on valence quarks

Inside a proton there are 3 valance quarks. In addition, there is constant creation and annihilation of gluon, quarks and anti-quarks. The number of virtual particles we observe depends on how ...
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The meaning of keeping the bare parameters fixed

So, this question concerns two different kinds of renormalization group equations. I would like some clarifications, if possible. The usual RG equations taught in QFT courses, like the ...
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Books/resources for statistical field theory

I was wondering if anyone knows good, approachable textbook or other resources about statistical field theory (topics like in Kardar's Statistical physics of fields: lattice models, mean field theory, ...
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Field renormalization of scalar Yang-Mills

In most books, one can find the field renormalization $Z_3$ in Yang-Mills with fermionic matter in the fundamental. In the $\overline{MS}$ scheme, tt is given by $$ Z_3 = 1 + \frac{g^2}{16\pi^2 ...
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Charge dependence of operators in QED renormalization

Consider a UV cutoff regulator $\Lambda$ with an effective QED lagrangian: $\mathcal{L}_{\Lambda} = \bar{\psi}_{\Lambda}(i\not \partial - m_{\Lambda})\psi_{\Lambda} - ...
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Introducing cut-off in a renormalisation procedure for quantum mechanics

I've been reading a paper on renormalisation theory as applied to a simple one-particle Coulombic system with a short-range potential. In the process of renormalisation, the authors introduce an ...
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Isolating the divergences in the stress energy tensor

In DeWitt's report "Quantum Field Theory in Curved Spacetime" (B. S. DeWitt, Phys. Rep. 19C, 292 (1975)), he states that in Eq.(175) $$\langle in, vac| T^{\mu\nu}|in,vac\rangle = 2 \frac{\delta ...
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Evaluation of the anomalous dimensions of fields in SUSY $SU(5)$

The general formula for the anomalous dimension can be found in Martin΄s review article (hep-ph/9709356), on page 62 relation (6.5.4). In the case of $SU(5)$ and especially in the paper of Kobayashi, ...
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What is the exact renormalization regularization for divergent harmonic serise?

given the harmonic series $$ \sum_{n=0}^{\infty}\frac{1}{n+a} $$ what is the correct option for the regularization ? a) $ \sum_{n=0}^{\infty}\frac{1}{n+a}= -\Psi (a) $ Digamma function b) $ ...
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Beta function of the non-linear sigma model

In chapter 7.1.1. inTong's notes about String Theory could someone sketch how can I show the statements that he nmakes around eq. 7.5 That the addition of the counterterm can be absorbed by ...
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One more time about LSZ-theorem

This question is the continuation of this one. For simplicity, let's use $(1)$ from the linked question (it is called n-point Green function and in particle case coincides with internal diagram), $$ ...
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Perturbative vs. non-perturbative approaches to a well-defined Yang-Mills theory in 4 dimensions

Another question regarding the Yang-Mills Existence and Mass Gap problem (http://www.claymath.org/sites/default/files/yangmills.pdf). Does the problem require that the "construction" of a four ...
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Do divergent parts cancel out between the 1-loop contribution to the vertex and the self-energy on the electron legs of the vertex diagram?

I regret I don't know how to draw Feynman diagrams here, so I refer to the standard book Peskin-Schroeder. At the beginning of section 7.5 on page 244 of this book several Feynman diagrams are shown, ...
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Apparent elimination of overlapping divergences

The integral, $$ \iint_{\mathbb{R}^{2+}}\frac{xy}{1+x+y} \mathrm{d}y \, \mathrm{d}x$$ possesses an overlapping divergence when $ x \to \infty $ and $ y \to \infty $. However, under a change of ...
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Reference for the renormalization of a scalar field's mass

There are a couple of interesting lectures by Leonard Susskind online, and in the first lecture on Supersymmetry & Grand Unification he explains renormalization. His example is the mass ...
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One-loop beta functions of the Standard Model

For my master's research on energy scale independent combinations of renormalization group equations in supersymmetric theories, I need an overview of all the one-loop beta functions of the Standard ...
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Running chargino/neutralino masses in MSSM

Consider the plot below, showing the running of different masses due to renormalization for a certain point of the (c)MSSM. I am able to exactly reproduce the plot, including the running of M1, M2, ...
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Beta function from exact renormalization group equation

I'm trying to calculate beta functions from exact (or functional) renormalization group equation (I mean Wilson-Polchinski RGE). I've got the equations but I don't know exactly how to use the ...
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Sharp cut-off, quadratic corrections and naturalness

When introducing the fine-tuning problem, a sharp cut-off as a regulator in the calculation of the Higgs mass corrections is used. Since this regulator breaks translational and gauge invariance, up to ...
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How to determine that the renormalization constant $Z_3$ must depend only on $g$ and $\Lambda/m$

In Le Bellac's book, Quantum and Statistical Field Theory, the renormalization constant $Z_3$ is introduced with the equation $$ \Gamma^{(2)}_R(k^2, m^2, g) = Z_3 \Gamma^{(2)}(k^2, m_0^2, g_0; ...
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Running of gauge couplings in the Standard Model [closed]

I'm sure many of us are familiar with the following plot showing the running of the inverse of the fine-structure constants of the SM. (I got the picture from google) At one-loop, the expressions ...
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Field Strength Renormalisation in Peskin and Schroeder

In chapter 7 of Peskin and Schroeder they define the field strength renormalisation $Z$ for a quantum field to be the residue of the Fourier transform of the correlation function $$\langle \Omega | ...
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RGEs of the MSSM - problems with Mathematica

I'm having some troubles with the trilinear soft couplings of the MSSM RGEs. I've used the ones written in Martin's supersymmetry primer and I run them using mathematica, if I do so without taking ...
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Renormalization, symmetries and freedom to choose counterterms

I am considering the perturbative renormalization of a simple non-phenomenological QFT with Lagrangian ${\cal L}$ (for scalar fields with multiple generations). I understand that I can renormalize it, ...
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Can a hierarchy of fixed points potentially be used to describe a kinetic energy spectrum which is composed of multiple scale invariant subranges?

Making use of a nonequilibrium functional renormalization group (Berges and Mesterhazy, 2012) are able to investigate a whole hierarchy of fixed points that explain the successive evolution of a ...
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IR divergence and renormalization scale in dimensional regularization (part 2)

This is in continuation of my previous question, IR divergence and renormalization scale in dimensional regularization. Lubos gave a nice answer there but I want to get to a very specific example ...
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Good reference for renormalization [duplicate]

Possible Duplicate: Are there books on Regularization at an Introductory level? I am looking for a good introduction to renormalization (group). I have read several books about it but never ...