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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Evaluate $1$-loop contribution to the $4$-point Green's function

I am trying to evaluate the following integral \begin{equation} I = \int \frac{d^d p_\text{E}}{(2 \pi)^d} \frac{1}{(p_\text{E}^2+m^2)((q_\text{E}-p_\text{E})^2 + m^2)} \tag{1} \end{equation} where ...
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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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393 views

Divergent Series

Why is it that divergent series make sense? Specifically, by basic calculus a sum such as $1 - 1 + 1 ...$ describes a divergent series (where divergent := non-convergent sequence of partial sums) ...
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667 views

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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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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Why do three dimensional gauge theories flow to conformal theories in the infrared?

What is meant with the fact that Super Yang-Mills flows to a conformal field theory in the infrared? Also, is this a general fact or does this depend on the fact of considering a certain class of ...
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132 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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226 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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Derivation of Eq. 7.12 in the review paper of Kraus

I'm reading "Lectures on black holes and the $AdS_3/CFT_2$ correspondence" by Kraus. http://arxiv.org/abs/hep-th/0609074 I don't know how one can obtain Eq.7.12. My stupid question is how to obtain ...
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535 views

Explanation of Cardy's “a theorem”

There seems to have been some discussion of Cardy's "a-theorem" recently: “It is shown that, for d even, the one-point function of the trace of the stress tensor on the sphere, Sd, when suitably ...
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190 views

Derivative with respect to ${\not}{p}$

When studying renormalization of QED in standard textbooks, we typically encounter derivatives with respect to ${\not}{p}=p^\mu \gamma_\mu$, i.e., $\partial/\partial{\not}p$. As far as I understand, ...
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121 views

The Euler equations as a RNG fixed point

In this paper at the at the beginning of the last paragraph on p.2 it is said, that the Euler equations, which are an infinite Reynolds number limit of the Navier-Stokes equations, arise as an RNG ...
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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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How do we know for sure a theory is non-renormalizable?

In quantum field theory, we are looking for a Lagrangian that is, amongst other, renormalizable. But how do we determine whether or not a theory is renormalizable? Is this purely done by power ...
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Equality of electric charges of all leptons

What does it precisely mean the often repeated statement that the electric charges of all leptons are the same. Let's consider QED with two leptons: electron and muon. The interaction part of the ...
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Some questions about the large-N Gross-Neveu-Yukawa model

Consider the following action with a fermionic field $\psi$ and a scalar field $\sigma$, $S = \int d^dx \{ -\bar{\psi}(\gamma^\mu \partial_\mu +\sigma )\psi + \Lambda^{d-4}[ \frac{(\partial_\mu ...
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If Renormalization Scale is Arbitrary, Why Do We Care about Running Couplings?

For the bounty please verify the following reasoning [copied from comment below] Ah right, so the idea is that overall observable quantities must be independent of the renormalization scale. But at ...
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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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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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Are irrelevant terms in the Kahler potential always irrelevant, even at strong coupling?

I've been reading about the duality cascade in Strassler's TASI '03 lectures (hep-th/0505153). He reminds us of the non-renormalization theorem theorem for the superpotential so that the beta ...
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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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Geometric entropy vs entanglement entropy (dependent on curvature coupling parameter)

I have a quick question. In hep-th/9506066, Larsen and Wilczek calculated the geometric entropy (which I believe is just another name for entanglement entropy) for a non-minimally coupled scalar field ...
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Is 'now' smeared over time?

Conventional physics as is usually presented in textbooks deals with the evolution of states in phase space parameterized by sharp instances in time, a real parameter. However, quantum fluctuations ...
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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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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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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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550 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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460 views

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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How do we measure the physical field of a particle?

In the renormalization procedure of quantum field theories, say $\lambda \phi^4$ theory for simplicity, we use the physical mass $m$, the physical coupling constant $\lambda$ and the physical field ...
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QED coupling constant at one loop

On page 257 in Peskin's QFT book a qualitative sketch of the QED coupling is given (see the picture below). Why should I expect such a behavior from QED? The QED beta function is ...
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Can we obtain non-Lorentzian metric from Lorentzian metric, through renormalization methods?

Since low-energy, non-relativistic thermal field theories are defined in Euclidean spacetime, while high-energy relativistic theories are define in Minkowski spacetime, I was wondering if there are ...
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116 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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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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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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Why is $\vert \phi \vert ^2$ infinite in QFT?

I've read here¹ that for a scalar field $\phi$, the square $\vert \phi \vert ^2$ is infinite (which gives an infinite contribution to mass), more precisely: the square of the field – a quantity ...
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Regularization and renomalization in the lightcone quantization of bosonic string

This question relates to this link. But I still don't understand it >_< In Polchinski's string theory vol I, p. 22, there is a divergence term (when $\epsilon \rightarrow 0$) in the zero point ...
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Zeta regularization and Renormalization group

Is there a physical method to prove for example when the zeta regularization of a series $$ 1+2^{k}+3^{k}+............= \zeta (-k) $$ gives the correct result: Casimir effect, vacuum energy and when ...
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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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431 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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532 views

Zeta-function regularization in QFT for heat kernels

When one is doing zeta-function regularization of the heat-kernel for QFT then one is doing these following steps, the integral over the imaginary time taking the trace of the heat-kernel or the ...
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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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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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$U(1)$ 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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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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Power counting with a cutoff

In Effective Field Theory video lectures found here, the professor explained power counting in effective field theories and the difficulties of power counting associated with loop diagrams. He then ...
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Could quarks be free in higher-dimensional space than 3D?

Reading this answer, I now wonder: if quarks are confined by $r^2$ potential, could their potential allow infinite motion in higher-dimensional space? To understand why I thought this might be ...
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Does the Renormalization of QFT Contradict Canonical Quantization?

Does the renormalization of QFT contradict canonical quantization? In canonical quantization, you take the classical fields and canonical momenta and turn them into operators, and you require that ...
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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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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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Derivatives of fluctuations about a condensate

Firstly I am not sure as to whether I am using the word "condensate" in the right context. In QFT contexts I think I see it getting used to mean the space-time independent solution which would solve ...