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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What's the difference between divergences that can be corrected and those that can't
I'm confused by renormalization . If a lagrangian has a term with negative mass dimension , why can't the divergences be absorbed into lagrangian coefficients? What's the difference between ...
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106 views
$U(1)$ beta function of low energy effective Seiberg-Witten theory
My question is about figure3 (page 8) of this paper
hep-th/9705131.
Start from Seiberg-Witten theory, integrate out the charged
high energy modes down to Higgs scale and we get a $U(1)$ gauge
theory ...
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47 views
Will Anderson's Poor Man's Scaling loose its effect when band width is small?
The s-d interaction Hamiltonian is as fellows
$H_I=Js.S$, J is the coupling strength.
We focus on the antiferromagnetic case, where $J>0$.
According Anderson's poor man's scaling, the ...
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218 views
Can scattering amplitudes be simplified with 1PI diagrams?
I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
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2answers
97 views
Determination of auxiliary scale in dimensional regularization
My questions are in italics. In the article [1] a dimensional regularization is presented on an electrostatic example of an infinite wire with constant linear charge density $\lambda$. It is shown ...
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1answer
192 views
Residues in QFT propagator
It is a well known fact that the location of the pole of a propagator (in QFT) can be interpreted as the physical mass.
Is there an interpretation for the residue of the propagator?
Note: I´m ...
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202 views
Reasons for violation of universality in statistical mechanics
The Universality in statistical mechanics is nicely explained by the renormalization group theory. However, there are fair amount of numerical and theoretical studies show that it can be violated in ...
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39 views
Linear combination of anomalous dimensions in effective potential on pseudomoduli space
In the paper of Intriligator, Seiberg, and Shih from 2007, they give an expression for the effective potential on the pseudo-moduli space $X$, estimated at large $X$ (equation 1.3).
In this equation, ...
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221 views
Quantum field theories with asymptotic freedom
QCD is the best-known example of theories with negtive beta function, i.e., coupling constant decreases when increasing energy scale. I have two questions about it:
(1) Are there other theories with ...
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1answer
78 views
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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1answer
154 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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1answer
402 views
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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184 views
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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1answer
284 views
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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1answer
148 views
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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103 views
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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60 views
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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0answers
78 views
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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322 views
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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3answers
252 views
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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1answer
353 views
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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1answer
76 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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77 views
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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4answers
172 views
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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118 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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1answer
151 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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1answer
468 views
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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396 views
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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2answers
258 views
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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0answers
54 views
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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60 views
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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1answer
169 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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1answer
147 views
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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156 views
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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1answer
286 views
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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94 views
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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1answer
111 views
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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1answer
241 views
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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592 views
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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2answers
156 views
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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119 views
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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1answer
95 views
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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100 views
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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1answer
95 views
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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2answers
376 views
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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103 views
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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1answer
192 views
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 ...
