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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Dimensional regularization: removing more than just logarithmic divergencies?

I have followed two courses on QFT, which both involved renormalization by dimensional regularization. My confusion is that one of the professors claimed that dimensional regularization can only be ...
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IR divergence and renormalization scale in dimensional regularization

Is it possible that if a certain (loop) integral is IR divergent then that will have effect on the dimensionally regularized answer for that? (..does the epsilon expansion see the IR divergence in ...
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489 views

What does it mean to renormalize an effective field theory?

This is in reference to slide 19 of this talk "As always in Effective Field Theory, the theory becomes predictive when there are more observables than parameters" Can one explain what this exactly ...
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223 views

Integrating out high momentum modes in $\phi^4$ theory

I'm trying to follow section 12.1 of Peskin & Schroeder, which describes how integrating out the high momentum modes of the field in $\phi^4$ theory transforms the Lagrangian both by changing the ...
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524 views

Anomalous dimension for bare actions with a standard kinetic term

In this paper on p42, it is explained that when starting with a bare action that contains a standard kinetic term, this kinetic term attains a correction in the course of the RG flow which can be ...
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256 views

How (why!?) does one introduce an UV cut-off in dimensional regularization?

This question is in reference to the confusing equation 3.7 (page 14) of this paper. One sees the 1-loop answers in their theory as given in their A.7 and A.8 on page 20. Each of the terms is a ...
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115 views

What is energy in $z \neq 1 $ theories?

In a critical theory with dynamical critical exponent $z \neq 1 $, which amongst frequency, $\omega$, and dispersion, $E(\vec{k})$, may be referred to as ''energy''? I'm confused about this since in ...
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What is the difference between scale invariance and self-similarity?

I always thought that these two terms are some kind of synonyms, meaning that if you have a self-similar or scale invariant system, you can zoom in or out as you like and you will always see the same ...
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Relevant operators in two dimensional O(n) models

The most general hamiltonian of a two dimensional $O(n)$ and $Z_2$ invariant statistical model can be written: $$ H=\int d^2 x \left[\frac{\nabla \mathbf{\phi}^2}{2} + \frac{m_0^2}{2}\mathbf{\phi}^2 ...
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223 views

Beta-function non-zero at classical level?

In Jaume Gomis's lecture 5 on CFT at Perimeter Institute, he says (at 27:40 minute mark) that the beta function, classically, of the $m^2$ parameter in massive $\lambda \phi^4$ theory is $$\beta(m^2) ...
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299 views

Setting of renormalization scale in field theory calculations

In dimensional regularization an arbitrary mass parameter $\mu$ must be introduced in going to $4-\epsilon$ dimensions. I am trying to understand to what extent this parameter can be eliminated from ...
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Can Divergences in Nonrenormalizable Theories Always Be Absorbed by (An Infinite Number of) Counterterms?

For example, consider the $\phi^3$ theory in $d=8$, with Lagrangian: $\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}-\frac{1}{3!}\lambda_{3}\phi^{3}$. In 8 ...
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Renormalizibility by power counting

When testing a theory for its renormalizability, in practice one always calculates the mass dimension of the coupling constants $g_i$. If $[g_i]>0$ for any $i$ the theory is not renormalizable. I ...
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174 views

Under what conditions are the renormalization group equations “reversible”?

As I understand it, the renormalization group is only a semi-group because the coarse graining part of a renormalization step consisting of Summing / integrating over the small scales (coarse ...
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613 views

Renormalization condition: why must be the residue of the propagator be 1

In on-shell scheme, one of the renormalization conditions is that the propagator, say, a scalar theory $$\frac{1}{p^2+m^2-\Sigma(p^2)-i\epsilon}$$ must have a unit residue at the pole of ...
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What is the relationship between complex time singularities and UV fixed points?

In this paper it is described how the turbulent kinetic energy spectrum and the flatness (a measure for intermittency) are governed by the position of the (dominant) singularities of the solutions of ...
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482 views

What constant varies in the fine structure constant?

Using the renormalization group approach, coupling constants are "running". If we apply this to the fine structure (coupling) constant, we do know that, e.g., at energies around the Z mass, $$\alpha ...
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186 views

physical importance of regularization in QFT?

The standard lore in QFT is that one must work with renormalised fields, mass, interaction etc. So we must work with "physical" or renormalised quantities and all our ignorance with respect to its ...
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Does the number of left handed chiral quark superfields always equal half the number of quark flavours?

In Weinberg's "The Quantum Theory of Fields Vol III" page 267 we're told that $n_f = 2N_f$. Where $n_f$ are the number of flavours and $N_f$ is the number of left chiral quark superfields (or the ...
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481 views

Infinite Energy of Point Charges (in the context of classical field theories)

In the context of classical physics,is there any renormalization method to avoid infinite energy of point charges?
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1k views

Degree of divergence of a Feynman diagram

I am studying the degrees of divergence of Feynman diagrams. I feel that I miss something but I don't really understand what. Please apologize if this question is silly. Anyway. As an introduction to ...
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370 views

Beta function of pure $SU(N_\text{c})$ Yang-Mills theory

What is the dependence of the beta function of pure $SU(N_\text{c})$ Yang-Mills theory on the number of colors? I guess ...
4
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957 views

One-loop $\phi^4$ theory in $d = 3$

I'm trying to calculate the 1 loop correction to the propagator in massless $\phi^4$ theory, in $d = 3$, just for fun. The diagram just looks like a straight line with a circle touching tangently to ...
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Why is Einstein gravity not renormalizable at two loops or more?

(I found this related Phys.SE post: Why is GR renormalizable to one loop?) I want to know explicitly how it comes that Einstein-Hilbert action in 3+1 dimensions is not renormalizable at two loops or ...
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What does it mean to integrate out fields from a theory?

I've done a fair bit of reading on this subject and I'm still confused about the basic principle of integrating out fields in QFT. When we have a function of 2 fields a and b, f(a,b), and we integrate ...
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372 views

Dimensional Regularization involving $\epsilon^{\mu\nu\alpha\beta}$

Is it possible to dimensionally regularize an amplitude which contains the totally antisymmetric Levi-Civita tensor $\epsilon^{\mu\nu\alpha\beta}$? I don't know if it's possible to define ...
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Why is $R^2$ gravity not unitary?

I have often heard that $R^2$ gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity? My naive ...
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Symmetries in Wilsonian RG (2)

This question is related to the paper http://arxiv.org/abs/1204.5221 and is a continuation of the previous question Symmetries in Wilsonian RG In the liked paper why do the equalities in equation ...
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Dimensional regularization and IR divergences and scale invariance

I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant. Does dimensional regularization see "all" kinds of divergences? I mean - what ...
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274 views

What states are satisfying an entropic area law and why do they satisfy it? More specificly why do matrix product states satisfy it?

I am currently reading some papers concerning the question why the density matrix renormalization group (DMRG) method is working well for simulating one dimensional systems and bad for higher ...
6
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296 views

Divergent sum in lightcone quantization of bosonic string theory

I had the following question regarding lightcone quantization of bosonic strings - The normal ordering requirement of quantization gives us this infinite sum $\sum_{n=1}^\infty n$. This is regularized ...
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379 views

Symmetries in Wilsonian RG

I wanted to know if there is a theorem that in writing a Lagrangian if one missed out a term which preserves the (Lie?) symmetry of the other terms and is also marginal then that will necessarily be ...
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335 views

Radial quantization and infrared divergences

I am reading Ginspard lectures "Applied CFT" http://arxiv.org/abs/hep-th/9108028 which is not my first material on the subject. He tries to motivates radial quantization on the reason that ...
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Regulator-scheme-independence in QFT

Are there general conditions (preservation of symmetries for example) under which after regularization and renormalization in a given renormalizable QFT, results obtained for physical quantities are ...
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Soft Mass and Physical Mass in Softly-broken SUSY

In softly broken SUSY, the bare mass parameters may be specified at e.g. the GUT scale, and then we can run these down to another scale using RGEs, similar in form to the RGEs for gauge couplings, ...
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Zeta regularization gone bad

This may sound as a mathematical question, but it should be very familiar to physicists. I am trying to perform an expansion of the function $$f(x) = \sum_{n=1}^{\infty} \frac{K_2(nx)}{n^2 x^2},$$ for ...
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294 views

Renormalization: Why is only a finite number of counter-terms allowed?

I have a question please about renormalization in QFT. Why a renormalizable theory requires only a finite number of counter-terms?
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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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Difference between a Fixed Point and a Limit Point in implementations of the Renormalization Group (RNG) in Large Eddy Simulation (LES) model

In the introduction of this paper, it is explained that and how the application of a dynamic subrid scale model for turbulence into a large eddy simulation (LES) model corresponds to doing one ...
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Why do irrelevant operators require infinitely many counterterms?

As far as I understand it, in the Wilsonian picture of renormalization, we view a theory as having some fixed cutoff and bare couplings, and integrate out high-momentum modes to understand what ...
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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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Can modern twistor methods to calculate scattering amplitudes be applied to renormalization group calculations?

As explained for example in this article by Prof. Strassler, modern twistor methods to calculate scattering amplitudes have already been proven immensely helpful to calculate the standard model ...
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Drawing the RG flow diagram

In real-space renormalization group how does one find the complete RG flow exactly, (not schematically)? I understand it needs to be done on a computer. For example, I have the ising model on a ...
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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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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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3answers
503 views

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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Dimensional transmutation in Gross-Neveu vs others

Firstly I don't know how generic is dimensional transmutation and if it has any general model independent definition. Is dimensional transmutation in Gross-Neveau somehow fundamentally different ...
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Exact Beta Functions in Statistical Mechanics

I'm looking for analytically solvable models in statistical mechanics (classical or quantum) or related areas such as solid state physics in which the beta function for a certain renormalization ...
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399 views

Defining a CFT using beta-functions

Won't it be correct to define a CFT as a QFT such that the beta-function of all the couplings vanish? But couldn't it be possible that the beta-function of a dimensionful coupling vanishes but it ...
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What is the physical meaning of this simplification to calculate the effective coupling constants for a Gaussian model with quartic interactions?

To calculate the effective coupling constants $u'_2(q)$ and $u'_4(q)$ of the effective Hamiltinian eq (4.9) of this paper $$ H' = -\frac{1}{2}\int\limits_q u'_2(q)\sigma'_q\sigma'_{-q} - ...