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 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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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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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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Unitarity and renormalizability

What is the difference between the unitarity of the theory and its renormalizability? Can we say that renormalizable theory is unitary after renormalization? The questions have arisen after I have ...
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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 any ...
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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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Renormalization, integrating out high momenta Wilson way

In equation $(12.5)$ in Peskin and Schroeder, they write out the generating function but leave out all quadratic terms of the form $\phi\hat{\phi}$ arguing that they vanish since Fourier ...
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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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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 ...
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Why is tree-level interaction between neutral scalar and photons non-renormalizable?

I've read that the decay of a neutral scalar particle into two photons, i.e., $$ S(p+q) \to \gamma(p) + \gamma(q) $$ can't happen via tree diagrams and instead is caused by loop diagrams (such as a ...
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Are critical exponents below and above the critical point always same?

The scaling relations don't distinguish the the critical exponents below and above the critical value. In the mean field level, I understand these critical exponents are same whatever one approaches ...
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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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A question about the implication of UV divergence in QFT

I have a basic question about the logic of renormalization in quantum field theory (QFT). We met the ultraviolet (UV) divergence in loop corrections. The standard argument is, our current field theory ...
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Is the effective Lagrangian the bare Lagrangian?

In standard (non-Wilsonian) renormalization we split the bare Lagrangian $\mathcal{L}_0$ into a physical Lagrangian $\mathcal{L}_p$ with measurable couplings and masses counterterms $\mathcal{L}_{...
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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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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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Quantum field theory defines its own bounds of applicability

I recall hearing in a lecture something along the following lines: "Due to some intrinsic feature of quantum field theory in general (or maybe it was the standard model?), we know where it is ...
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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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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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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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Top quark mass $m_t$ at energy scales $\mu < m_t$?

Edit - Maybe formulated differently: Does it make sense to talk about the top mass at energies below $m_t$, although in all processes the corresponding energy scale is above $m_t$, because of the rest ...
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Energy scale dependence of coupling constants

I am trying to understand the meaning of the renormalization group equation and what i have understood is that, since observable (or physical?) quantities must not depend on arbitrary energy scales, ...
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Why doesn't a renormalizable $\phi^4$ theory have odd diagrams?

I've been reading Zee's QFT textbook and trying to follow some lecture notes online whenever I can't grasp something. I really don't understand one thing regarding the renormalization of theories, ...
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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-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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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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Superficial degree of divergence on Weinberg

Reading volume 1 of Weinberg's QFT book, chapter 12, page 505 he says that if you consider a diagram with degree of divergence $D\geq{}0$, its contribution can written as a polynomial of order $D$ in ...
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Renormalization in Classical Field Theory

1) The statement that general relativity (GR) is not renormalizable - is it a statement only about the quantization of GR or is it non-renormalizable also as a classical field theory? 2) More ...
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$U(1)$ abelian/axial/chiral anomaly in 4D

I am reading $U(1)$ abelian/axial/chiral anomaly in 3+1 dimensions using the path integral method (Fujikawa). Am I wrong in assuming that the anomaly can be cancelled by introducing a counter term 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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Renormalization and the Hierarchy Problem

The hierarchy problem is roughly: A scalar particle such as the Higgs receives quadratically divergent corrections, that have to cancel out delicately with the bare mass to give the observed Higgs ...
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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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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 ...
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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 C_i^{(\...
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Have experiments ever suggested two different values to the same divergent series?

I believe to have understood that some physical experiments suggest finite values to divergent series (please correct me if I'm wrong, my understanding of these matters is limited). I heard, for ...
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Logarithms in Renormalization

I am learning renormalization in Quantum field theory and following mainly Schwartz (Quantum field theory and standard model) for it. While explaining Renormalization group equations it says it mainly ...
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What should I think of a diverging beta function (in Renormalisation Group flow)?

I have written a set of RG flow equations using Functional Renormalisation Group methods. I am looking at the flow of a well known problem with an additional original coupling. I did not do anything ...
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Symmetry of interaction lagrangian and symmetry of full lagrangian

Suppose we have lagrangian $$ \tag 1 L = \frac{\theta}{f_{\gamma}}F_{EM}\tilde{F}_{EM} +\frac{1}{2}(\partial_{\mu}\theta)^2 - \frac{1}{2}m_{\theta}^2\theta^2 + L_{SM}, $$ where $\tilde{F}_{EM}$ ...
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Determinant of a propagator

Say I have a path integral $\int D \phi \exp(i S_0)$. $S_0$ is the usual free action $$S_0=\frac{1}{2}\int\phi (-\Box-m^2) \phi=\frac{1}{2}\int \phi G^{-1} \phi,$$ and at the moment I'm not ...
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How to handle the infrared divergence of massless $\phi^4$ in scattering

For massless $\phi^4$ theory, if exterior momentums are going to zero, then this diagram will be $$\int \frac{dk^4}{k^4}$$ will suffer from infrared divergence. Because the infrared divergence, ...
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Is there a maximum number of fixed points that a QFT can have?

I was wondering: is there a maximum number of (trivial and non-trivial) fixed points that a QFT can have (as a function of the space-time dimension and field content in the QFT)?
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Renormalization of Auxiliary Fields

I have the following non-linear sigma model (the base space $\mathcal{M}$ is Euclidean): $$ \mathcal{L}=\dfrac{1}{2\alpha}\int_{\mathcal{M}}\mathrm{d}^2\sigma\ \partial^2X^{\mu}\partial^2X_{\mu} $$ ...
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Which cardinality of infinities are subtracted in the renormalisation of quantum field theory?

In quantum field theory, e.g. in quantum electrodynamics, renormalisation is used to make sense of an infinite number of virtual particles. This, crudely, involves the subtraction of infinities. But ...
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Wilson's Renormalization Group and Lie's Third Theorem

If you think of a one-parameter group of transformations along a curve in the plane as a (Lie) group, and the tangent vector to the curve as a generator of the curve we can intuitively understand Lie'...