Renormalization is an ensemble of techniques which serves to treat the infinities which appear in quantum field theory or statistical mechanics.

learn more… | top users | synonyms (1)

2
votes
0answers
109 views

Neglecting mass at asymptotic spacelike momenta

What is the rational/reason for neglecting masses at asymptotic non-exceptional space-like momenta. I have come across this as a first fix for being able to extract information from the ...
6
votes
1answer
297 views

Divergent bare parameters/couplings: what is the physical meaning of it? Do this have any relation with wilson's renormalization group approach?

I understand that bare parameters in the Lagrangian are different from the physical one that you measure in an experiment. I'm wondering if the fact that they are divergent has any physical meaning? ...
0
votes
1answer
61 views

Assymptotic freedom significance

So I have read a bit on this, and get the idea and mathematical machinery leading up to this. I get that it sheds light on the relationship between coupling strengths and length scales. Can someone ...
2
votes
1answer
180 views

Quantum corrections to massless fermionic field

in QED the corrections to electron propagator change the bare electron mass from $m_0$ to $m=m_0+δm=m_0+∑(\not{p}=m)$ (Peskin, formula 7.27). This is the consequence of the fact, that the quantum ...
5
votes
1answer
99 views

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 ...
0
votes
0answers
93 views

Renormalization beta-function

I want to know the other forms of beta-function that make manifest certain properties of renormalization group, for instance dependence on poles/residue and more. If possible can you state a ...
5
votes
2answers
771 views

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 ...
6
votes
2answers
187 views

No non-trivial UV asymptotically free and IR free

How it could be proven that a non-trivial theory cannot be both asymptotically free and IR free (g=0 both in the UV and IR with some interpolating function in between)? This is of course contrary to ...
1
vote
1answer
97 views

independence of the bare parameters on μ for beta function

So I know re-normalization has bean "beaten to death". I want to understand something a bit specific which might seem trivial. Independence of the bare parameters on $\mu$ and relevance to the beta ...
8
votes
1answer
856 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) ...
3
votes
2answers
4k views

How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”? [duplicate]

How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”, in the context of physics? I heard Lawrence Krauss say this once during a debate with Hamza Tzortzis ...
29
votes
5answers
1k views

What exactly is regularization in QFT?

The question. Does there exist a mathematicaly precise, commonly accepted definition of the term "regularization procedure" in perturbative quantum field theory? If so, what is it? Motivation and ...
2
votes
0answers
78 views

How to show that tensor gravity is nonrenormalizable?

Let's have the tensor gravity theory, which represented the massless spin-2 field: $$ L = -\frac{1}{32 \pi G}\left( \frac{1}{2}(\partial_{\alpha}h_{\nu \beta}) \partial^{\alpha}\bar {h}^{\nu \beta} - ...
7
votes
1answer
357 views

Basic question about the S-Matrix, Unitarity and Effective Field Theory

Consider scattering some particles in a state collectively denoted by $i$ to a final state denote by $f$. The scattering amplitude, S-matrix is then defined by: $S_{fi}\equiv \langle ...
6
votes
1answer
259 views

Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section ...
2
votes
1answer
75 views

Explicit calculation of bosonic string Weyl invariance at one loop

I have been trying to do all the calculations in the Green, Schwarz and Witten Superstring Theory textbook. At the end of chapter 3, the author did one-loop calculation for Weyl invariance for the ...
5
votes
1answer
202 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, ...
8
votes
1answer
542 views

Where does the divergence in the $g\phi^3$ $d=4$ 3 point one loop diagram (three external legs) come from?

$g\phi^3$ , $d=4$ , 3 point One loop diagram (three external legs) Divergence I am trying to find where the divergence factor/pole is on the following diagram in 4 dimensions so that I can use ...
6
votes
2answers
311 views

Semantic problem about renormalizability

This post relates to this previous one. My question is, what is the actual meaning of a theory being renormalizable? There might be at-least two possibilities (correct me if I am wrong) ...
1
vote
0answers
255 views

One-loop beta functions of the Standard Model

For my master's research on energy scale independent combinations of renormalization group equations in supersymmetric theories, I need an overview of all the one-loop beta functions of the Standard ...
1
vote
0answers
97 views

Running chargino/neutralino masses in MSSM

Consider the plot below, showing the running of different masses due to renormalization for a certain point of the (c)MSSM. I am able to exactly reproduce the plot, including the running of M1, M2, ...
1
vote
1answer
152 views

Amplitudes in renormalized perturbation theory

This question arose while reading Peskin and Schroeder, specifically, it arose in regards to the sum of diagrams above their Eq. (10.20) on pg. 326. The context is $\phi ^4$ theory and they are using ...
3
votes
0answers
98 views

Link between anomalous dimensions and fractal dimensions

I just realized that anomalous dimensions in quantum/statistical field theory is not that different from fractal dimensions of objects. They both describe how quantitaive objects transform under a ...
2
votes
1answer
273 views

Why does the counterterm's propagator have inverse units of the propagator? $\phi^4$-theory

According to Peskin & Schroeder (page 325), the Feynman rule for the counterterm ------(x)----- for $$ \frac12 ...
5
votes
1answer
157 views

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 ...
3
votes
3answers
270 views

Renormalization of Composite Chiral Superfields

On page 24 of these lecture notes http://arxiv.org/abs/hep-th/0309149 it is stated that products of chiral superfields do not suffer from short distance singularities. In other words, if I want to ...
-1
votes
1answer
119 views

Why isn't renormalization called dark physics?

In QED there is extra energy that has to be gotten rid of to match observations. Kind of the opposite to GR/ND where you have to add extra energy/matter to match observations. Why isn't ...
2
votes
1answer
144 views

Misunderstanding Wick Ordering

In M. Salmhofer's "Renormalization, An Introduction" Wick ordering is defined as follows: Let $C = C_\Gamma$ be a nonnegative symmetric operator on $\mathbb{C}^\Gamma$. For $J: \Gamma \to ...
0
votes
1answer
130 views

IR non-renormalizable theory

can be a theory with an infinite number of divergent integrals of the form $$ \int \frac{d^{p}k}{k^{m}} $$ for m=1 , 2 , 3 , 4 ,...... so the theory would be IR non renormalizable and you would need ...
1
vote
0answers
407 views

Beta function from exact renormalization group equation

I'm trying to calculate beta functions from exact (or functional) renormalization group equation (I mean Wilson-Polchinski RGE). I've got the equations but I don't know exactly how to use the ...
6
votes
0answers
602 views

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 ...
61
votes
1answer
2k views

Does the 4/3 problem of classical electromagnetism remain in quantum mechanics?

In Volume II Chapter 28 of the Feymann Lectures on Physics, Feynman discusses the infamous 4/3 problem of classical electromagnetism. Suppose you have a charged particle of radius $a$ and charge $q$ ...
3
votes
1answer
192 views

What happens when you apply the path integral to the Einstein-Hilbert action?

The Einstein Field Equations emerge when applying the principle of least action to the Einstein-Hilbert action, and from what I understand the path integral formulation generalizes the principle of ...
3
votes
1answer
498 views

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 ...
1
vote
0answers
96 views

Sharp cut-off, quadratic corrections and naturalness

When introducing the fine-tuning problem, a sharp cut-off as a regulator in the calculation of the Higgs mass corrections is used. Since this regulator breaks translational and gauge invariance, up to ...
9
votes
1answer
388 views

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
votes
1answer
219 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 ...
3
votes
1answer
251 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 ...
10
votes
2answers
598 views

Why are only logarithmic divergence relevant for the Callan-Symanzik equation? Intuitive understanding?

I may be wrong, but it seems that only logarithmic divergences need to be retained when using the Callan-Symanzik equation, finding running couplings, etc. Why is this the case? Is there some simple ...
6
votes
1answer
157 views

Renormalizability of the Polyakov Action

I was told today that the Polyakov action for a $p$-brane is (superficially) re-normalizable iff $p\leq 1$. Of course, when I went to check for myself, I screwed up my power-counting, and I'm having ...
16
votes
1answer
643 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 ...
3
votes
0answers
118 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 ...
8
votes
0answers
212 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
votes
1answer
279 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
votes
1answer
406 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 $\Gamma^{(2)}$ ...
1
vote
0answers
50 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; ...
7
votes
1answer
413 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 ...
4
votes
1answer
126 views

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 ...
1
vote
1answer
78 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 ...
11
votes
1answer
664 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 ...