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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Freedom in the Choice of a Beta Functions in RG

Assume we're given a certain statistical model, say the infinite range Ising model \begin{equation} H_{N}\{\vec\sigma_{N}\}~=~ - \frac{x_{N}}{2N} \sum_{i,j =1}^{N} \sigma_{i} \sigma_{j} ...
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Evaluating propagator without the epsilon trick

Consider the Klein–Gordon equation and its propagator: $$G(x,y) = \frac{1}{(2\pi)^4}\int d^4 p \frac{e^{-i p.(x-y)}}{p^2 - m^2} \; .$$ I'd like to see a method of evaluating explicit form of $G$ ...
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288 views

Is proper time renormalization gauge invariant?

Proper Time Renormalization is achieved by putting: $$ \int_0^\infty e^{iat} dt = {1\over ia} $$ Is it true that this is the only kind of normalization that is gauge invariant? If so, why do famous ...
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Multi-loop beta function of gauge theory (*without* Feynman diagrams)

I would like to point to the beautiful section 4.3 (page 42) of these lecture notes. I think this is the most educative exposition I have ever seen anywhere about Yang-Mill's beta function. What I ...
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What is the exact relationship between scale invariance and renormalizability of a theory?

I have often read that renormalizability and scale invariance are somehow related. For example in this tutorial on page 12 in the first sentence of point (7), self similarity (= scale invariance ?) is ...
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Why is mass renormalization insufficient to explain electron mass?

In the Standard Model, I understand that the mass of the electron is assume to arise from two effects: A bare mass given by Yukawa interaction with the Higgs field, and A mass correction from mass ...
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Renormalization of field strength

I'm revisiting the elementary algorithms of renormalization that are taught in a classroom setting and find that the procedure taught to students is as follows: Write down the bare Lagrangian: ...
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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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Wilsonian vs 1PI

As a follow up to Difference between 1PI effective action and Wilsonian effective action, where can I find pedagogical material that highlights the similarities and differences between the 1PI and ...
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SU(2) critical point and volume dependence

I am doing multi-dimensional plots of $\beta_j$ for SU(2) for infinite volume to understand the flow behavior and I was wondering, before I go too much further, if anyone knew off the top of their ...
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Superstring theory and renormalization [duplicate]

Possible Duplicate: Does the renormalization group apply to string theory? Renormalization in string theory QED and some quantum theories require renormalization techniques and take it as ...
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How can perturbativity survive renormalization?

The most usual way to renormalize quantum field theories is by re-writing the Lagrangian in terms of physical (finite) parameters plus counter-terms. Take $\lambda \phi^4$ theory for instance: $$ ...
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What is the 'quantum-developed' or 'relativistic-developed' equation of the electrostatic force?

Quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics that is the first theory where full agreement between quantum mechanics, special relativity and ...
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About calculation of anomalous dimension in Peskin and Schroeder's book.

This question is in reference to question 13.2 in the QFT book by Peskin and Schroeder. To put it in general - I would like to know how does one define "anomalous dimensions" if one is given the ...
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87 views

Numerical renormalization

is there a numerical algorithm (Numerical methods) to get 'renormalization' ?? i mean you have the action $ S[ \phi] = \int d^{4}x L (\phi , \partial _{\mu} \phi ) $ for a given theory and you want to ...
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mathematical explanation for UV divergences and $ \delta ^{(n)}(0) $

is there any mathematical explanation for the UV divergences ?? i have read that in the framework of Epstein-Glser theory :D these UV divergences appear from the product of distributions anyone does ...
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Is there a non-perturbative remormalization? If so, how does it work?

Is there a method to renormalize a theory without using perturbative expansions for the divergences? For example, is there a method to get masses and other renormalized quantities without using ...
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160 views

What is the Principle of Maximum Conformality?

I'm trying to understand this article about an advance in the theoretical understanding of QCD which centers on the Principal of Maximum Conformality. What is this Principle? In other words, what is ...
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308 views

Pedagogic reference for calculation of 2-loop anomalous dimension (supersymmetric)

I want to know of pedagogic references which teach how to compute anomalous dimensions (..wave-function renormalization..) at lets say 2-loops. I guess there might be specialized techniques for ...
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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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Why is GR renormalizable to one loop?

I have read in a few places that GR is renormalizable at one loop. (hep-th/9809169 for example, second sentence, although they don't seem to develop this point at all). Is this do to some hidden ...
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Is QCD free from all divergences?

On page 8 in http://arxiv.org/pdf/hep-th/9704139v1.pdf David Gross makes the following comment: "This theory [QCD] has no ultraviolet divergences at all. The local (bare) coupling vanishes, and the ...
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is cosmic expansion related with IR divergencies?

This question is related to renormalization, but in the IR limit. It is assumed that unitarity does take care of IR divergencies in interacting theories like QED. But how would one interpret ...
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Relating the deformation of Calabi-Yau metrics and the conformal quantum field theories

(v2) As I read e.g. in this question, the nice holonomy group features of Calabi-Yau manifolds are valuable regarding supersymmetry (I suspect because it's a symmetry involving the target manifold, ...
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289 views

Quantum gravity and relevant/irrelevant operators

I am familiar with the casual dichotomy in QFT between coupling with positive dimensions in energy implies relevant operator on one side and negative dimension implies irrelevant operator on the other ...
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Is every QFT non-local in the U.V.?

As much as I understand the renormalization group transformation and the concept of relevant/irrelevant operators, I'd say that if we push the reasoning of only looking at relevant operators when we ...
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Any link between decoherence and renormalization?

I have been studying decoherence in quantum mechanics (not in qft, and don't know how it is described there) and renormalization in QFT and statistical field theory, I found at first a similarity ...
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A certain regularization and renormalization scheme

In a certain lecture of Witten's about some QFT in $1+1$ dimensions, I came across these two statements of regularization and renormalization, which I could not prove, (1) $\int ^\Lambda \frac{d^2 ...
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Does the measure of proximity of two theories in “theory space” run?

From reading this article, I have learned that two effective QFTs can be very close together in the "theory space" appropriate to describe for example physics at the LHC scale, whereas the ...
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renormalization group in d=3

Do we really understand why the renormalization group in $d=2+\varepsilon$ and $d=4-\varepsilon$ taking $\varepsilon=1$ gives "good" values for critical exponents in $d=3$? Are they exceptions? Is it ...
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What is the meaning of the concepts of “operator mixing” (and anomalous dimensions) [closed]

I am looking for an explanation about the idea of "operator mixing" and its associated concept about when anomalous dimension has to be thought of as a matrix. For example this idea is slightly ...
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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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How to deal with the product of distributions by Renormalization or similar?

how can we deal for example with the product of distributions in physics ?? is there any mean to define with physics $ \delta ^{2}(x) $ or to treat a product of two distributions within the ...
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Could motives aid in the study of the Navier-Stokes equations?

Recently, mathematicians and theoretical physicists have been studying Quantum Field Theory (and renormalization in particular) by means of abstract geometrical objects called motives. Amongst these ...
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Intuitive picture for spin-fluctuations contribution to specific heat of He3

Usually when discussing Fermi liquid theory, it is stated that due to the quasiparticles effectively behaving like a free electron gas with effective mass, the specific heat is linear in $T$ at small ...
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From vertex function to anomalous dimension

In a $d$ dimensional space-time, how does one argue that the mass dimension of the $n-$point vertex function is $D = d + n(1-\frac{d}{2})$? Why is the following equality assumed or does one prove ...
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Instantons and Borel Resummation

As explained in Weinberg's The Quantum Theory of Fields, Volume 2, Chapter 20.7 Renormalons, instantons are a known source of poles in the Borel transform of the perturbative series. These poles are ...
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Renormalization of the R-charge?

In general I would like to know as to known or what is/are the standard references about R-charge renormalization in supersymmetric theories. When does it do so and what is expected or known to be ...
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Why are conformal transformations so prevalent in physics?

What is it about conformal transformations that make them so widely applicable in physics? These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
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Is the form of the Lagrangian relevant before the renormalization procedure?

In the renormalization procedure, is writing things like $$\varphi=\sqrt{Z_{\varphi}}\ \varphi_R\ ,\ \ m_0^2=Z_m\ m_R^2\ ,\ \ g_0=Z_g \mu^{\epsilon}\ g_R$$ and $$Z_i=1+\sum_{\nu=1}^\infty ...
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What's the meaning of the coupling change after a renormalization (in the 1-dim Ising Model)?

What does it mean that after the theory (1-dim Ising model here, but the question is general) is renormalized one time and $g_i\rightarrow g_i'$, that the couplings are weaker, even if the theory ...
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How is the apparent significance of (length) scales in physics explained?

From what I understand, especially from reading arguments on Physics.SE, different (length) scales of a system are extremely important. It's clear that if there are two scales $\delta,d,D,\Delta$ with ...
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Scaling with the Ising Model

I am stuck with one formula in the CFT book by Di Francesco and al. Chapter 3. Equation 3.46 third step, for those who don't have the book, he integrates out degrees of freedom from the Ising Model by ...
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How to perform a scale (invariance) transformation?

According to this wikipedia article in the $\phi^4$ section, the equation $$\frac{1}{c^2}\frac{∂^2}{∂t^2}\phi(x,t)-\sum_i\frac{∂^2}{∂x_i^2}\phi(x,t)+g\ \phi(x,t)^3=0,$$ in 4 dimensions is invariant ...
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Significance of massive states in string theory

A free superstring has an infinite tower of states with increasing mass. The massless states correspond to the fields of the corresponding SUGRA. In "Quantum Fields and Strings: A Course for ...
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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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Question about the perturbative renormalization group

I'm currently learning about the renormalization group (RG) in condensed matter physics and just want to clarify a couple of things: When doing the RG transformation, there's a flow to a fixed point. ...
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Why is a gaussian fixed point called gaussian?

I know what a gaussian fixed point is, and I did read the wikipedia entry, but it wasn't helpful. It says because the probability distribution is gaussian, but what probability distribution?
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Values of SM parameters at one certain scale

The general question is: What are the values of Standard Model parameters (in the $\bar{MS}$ renormalization scheme) at some scale e.g. $m_{Z}$? As its parametrization in Yukawa matrices is not unique ...
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How can one build a multi-scale physics model of fluid flow phenomena?

I am working on a problem in Computational Fluid Dynamics, modeling multi-phase fluid flow through porous media. Though there are continuum equations to describe macroscopic flow (darcy's law, ...