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 definition of a “UV-complete” theory?

I would like to know (1) what exactly is a UV-complete theory and (2) what is a confirmatory test of that? Is asymptotic freedom enough to conclude that a theory is UV-complete? Does it become ...
3
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160 views

Ambiguity in Beta Functions (2-loop)

Beyond one-loop, the beta function of a QFT is scheme dependent. I would like to understand better this ambiguity. The easiest thing to say is that you haven't calculated something physical, so of ...
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194 views

Does effective theory have the same meaning in particle and condensed matter physics

I have a naive question about the meaning of effective theory in particle physics and condensed matter physics. In particle physics, from what I know, the effective theory comes from the Wilsonian ...
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538 views

What does it mean for a QFT to not be well-defined?

It is usually said that QED, for instance, is not a well-defined QFT. It has to be embedded or completed in order to make it consistent. Most of these arguments amount to using the renormalization ...
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86 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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105 views

Why do people rule out zeta regularization for renormalization?

Using zeta regularization one can get a formula for regularizing the integral $ \int_{a}^{\infty}x^{m-s}\text dx $ for any $m$. However, I have not seen anywhere. For example, I do not know why in ...
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153 views

Gauge fields in Polyakov's treatment of renormalization for nonlinear sigma model

I am deriving the results of renormalization for nonlinear sigma model using Polyakov approach. I am closely following chapter 2 of Polyakov's book--- ``Gauge fields and strings''. Action for the ...
8
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1answer
110 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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263 views

What are the details of the renormalization of Chern-Simons theory?

What is a good, simple argument as to why Chern-Simons theory' is renormalisable? Any good books/references dealing with this effectively? Why does the $\beta$-function vanish? Thanks!
3
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233 views

Two Loop ultraviolet divergence of $\phi^4$ theory

During the renormalization procedure of a massive $\phi^4$ theory at two loop level, one finds that the quantity $K_{\Lambda}(k^2,m^2)-K_{\Lambda}(0,m^2)$ that appears in the bare $\Gamma^{(2)}$ ...
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351 views

Why is renormalization necessary in finite theories?

Michael Brown made the following comment here: The modern understanding of renormalization (due to Kadanoff, Wilson and others) is hardly controversial and has nothing really to do with ...
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46 views

How to determine that the renormalization constant $Z_3$ must depend only on $g$ and $\Lambda/m$

In Le Bellac's book, Quantum and Statistical Field Theory, the renormalization constant $Z_3$ is introduced with the equation $$ \Gamma^{(2)}_R(k^2, m^2, g) = Z_3 \Gamma^{(2)}(k^2, m_0^2, g_0; ...
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71 views

Nonequilibrium themal QFT

Wick rotation to thermal of QFT in Minkowski space to thermal QFT, which is after this transformation analogue to statistical mechanics, does only describe equilibrium statistical mechanics. On page ...
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478 views

How does the Ward-Takahashi Identity imply that non-transverse photons are unphysical in QED?

Peskin and Schroeder say that the Ward Identity of QED proves that non-transverse photon polarizations can be consistently ignored, but I'm confused about the details. Setup One starts by ...
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405 views

Running of gauge couplings in the Standard Model [closed]

I'm sure many of us are familiar with the following plot showing the running of the inverse of the fine-structure constants of the SM. (I got the picture from google) At one-loop, the expressions ...
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276 views

Charge Renormalization and Photon Propagator

I'm trying to understand charge renormalization in QED. I know that one can write the full photon propagator as $$\frac{-i\eta_{\mu\nu}}{q^2(1-\Pi(q^2))}$$ where $\Pi$ is regular at $0$. Obviously ...
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139 views

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 ...
2
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95 views

Caimir effect regularization for every divergent sum or series

can we use the tools of renormalization of casimir effect to get finite results for any divergent series in QFT ?? for example let be the divergent series $ \sum_{n=1}^{\infty}n^{l} $ for positive ...
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278 views

How do fermion and scalar masses run with energy? Is the difference in their running the core of the hierarchy problem?

Do fermion and scalar running masses run in the same way? Specifically, what are the qualitative differences in the mass beta functions for, say, scalar $\lambda\phi^4$ field theory and the fermion ...
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QM and Renormalization (layman)

I was reading Michio Kaku's Beyond Einstein. In it, I think, he explains that when physicsts treat a particle as a geometric point they end up with infinity when calculating the strength of the ...
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196 views

Field Strength Renormalisation in Peskin and Schroeder

In chapter 7 of Peskin and Schroeder they define the field strength renormalisation $Z$ for a quantum field to be the residue of the Fourier transform of the correlation function $$\langle \Omega | ...
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125 views

RGEs of the MSSM - problems with Mathematica

I'm having some troubles with the trilinear soft couplings of the MSSM RGEs. I've used the ones written in Martin's supersymmetry primer and I run them using mathematica, if I do so without taking ...
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157 views

Renormalization, symmetries and freedom to choose counterterms

I am considering the perturbative renormalization of a simple non-phenomenological QFT with Lagrangian ${\cal L}$ (for scalar fields with multiple generations). I understand that I can renormalize it, ...
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291 views

Etymology of “Renormalisation”

Just out of curiosity, does anyone know why "renormalisation" is so named? Who first came up with the term, and why was it used? I did a mathematics undergraduate so to me "normalisation" means ...
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Renormalization Group for non-equilibrium

For equilibrium/ground state systems, a (Wilson) renormalization group transformation produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such ...
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111 views

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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215 views

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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159 views

Is the Schwinger action principle important in renormalization?

Is the Schwinger action principle important in renormalization? I want to know if this principle could help us to see if a model is renormalizable of not. If you have any other comment or information ...
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2answers
363 views

Is the big desert hypothesis a wilder assumption than the see-saw mechanism to explain neutrino masses?

Sometimes I see comments about the big desert hypothesis that I don't understand. For instance in a famous blog : ...This is based on a renormalization group calculation extrapolating the Higgs ...
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532 views

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 ...
6
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196 views

Naturalness arguments and dimensional regularization?

How do issues of naturalness arise when regularizing QFT using dimensional regularization? I can only recall ever seeing naturalness arguments (hierarchy problem, cosmological constant problem, etc.) ...
12
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554 views

The divergence in QCD Series— How many are they, and what do they mean?

I am referring to this question, and especially this answer. In addition, QCD has - like all field theories - only an asymptotic perturbation series, which means that the series itself will ...
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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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434 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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436 views

Renormalization is a Tool for Removing Infinities or a Tool for Obtaining Physical Results?

Quoting Wikipedia: renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities. Is that true? to me, it seems better to define ...
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Can a hierarchy of fixed points potentially be used to describe a kinetic energy spectrum which is composed of multiple scale invariant subranges?

Making use of a nonequilibrium functional renormalization group (Berges and Mesterhazy, 2012) are able to investigate a whole hierarchy of fixed points that explain the successive evolution of a ...
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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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466 views

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 (part 2)

This is in continuation of my previous question, IR divergence and renormalization scale in dimensional regularization. Lubos gave a nice answer there but I want to get to a very specific example ...
3
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204 views

Nonpertubative renormalization in quantum field theory versus statistical physics

I am trying to work my head around how renormalization works for quantum field theory. Most treatments cover perturbative renormalization theory and I am fine with this approach. But it is not the ...
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787 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 ...
2
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230 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 ...
4
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132 views

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 ...
2
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1answer
430 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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652 views

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 ...
3
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315 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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173 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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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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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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How to prove equivalence of RG flow of QFT coupling constant and diagrammatic resummation at fixed renormalization scale?

QFT books say that solving the RG equation $\frac {dg} {d\textbf{ln} \mu}=\beta(g)$, using the one-loop beta function, is to the "leading log" approximation equivalent to resumming infinitely many ...