Renormalization Definition and 174 Threads

Hi all, Can anyone tell me whether the counterterms introduced in renormalized perturbation theory (see e.g. Chapter 10 of Peskin and Schroeder) have any physical interpretation? In particular, are they taken to model the self-interactions that take us from a 'bare' to a 'dressed' particle...

I would like to ask if anyone can give me a hand with the understanding of the counterterms. I am reading by myself Chapter 10 of Peskin & Shroeder and got stuck in the middle of their example of how to renormalize \phi^{4} theory. What is puzzling me is how to obtain from the new Lagrangian...

Hello everybody, I have a short question about the renormalization scale. For dimensional regularization we introduce a scale μ with mass dimension to preserve the correct mass-dimension for the coupling and so on so that it is independent of the value of d = 4-2ε. But why can that μ have any...

In conventional renormalization one is first supposed to compute a scattering amplitude of interest in terms of bare quantities ##\lambda_0, m_0...##, then compute these bare quantities in terms of physical quantities, i.e. ##m(m_0,\lambda_0,...), \lambda(m_0, \lambda_0,...)## and substitute...

http://arxiv.org/abs/1305.6315 Why gravity codes the renormalization of conformal field theories Henrique Gomes, Sean Gryb, Tim Koslowski, Flavio Mercati, Lee Smolin (Submitted on 27 May 2013) We give a new demonstration that General Relativity in d+1 dimensions with negative or positive...

Hi. I have observed that Ryder in his book on QFT before doing dimensional regularization introduces a scale ##\mu## in order to keep the coupling constant dimensionless in the lagragnian. However in two other books; Weinberg and Peskin and Schroeder, they do not introduce this scale in the same...

From what I now understand of renormalization it is really a reparametrization of the theory in terms of measurable quantities instead of the 'inobservable bare quantities' that follow the Lagrangian; at least that is one interpretation of what is going on. The originally divergent physical...

In Peskin and Schroeder at page 323 second paragraph the author state 'To obtain finite results for an amplitude involving divergent diagrams, we have so far used the following procedure: Compute the diagrams using a regulator to obtain an expression that depends on the bare mass (m0), the...

In the textbook, usually the fermion mass renormalization is introduced as follows: the mass shift \delta m must vanish when m_0=0. The mass shift must therefore be proportional to m_0. By dimensional analysis, it can only depend logarithmically on \Lambda (the ultraviolet cutoff): \delta m \sim...

I did not understand one thing: imagine we have calculated a cross section relates to a process, for example compton scattering. The parameters (charge, mass, ...) that come into play in cross section are "bare parameters"? Then after the renormalization of the theory, getting the "bare...

I am confused about the idea of mass renormalization in quantum field theory. Firstly, in case of charge renormalization there is a picture where you have a swarm of particle antiparticle pairs round the electron and hence depending on the energy of your probe , the charge gets renormalized...

Hi, I will be writing my bechelors thesis on the application of renormalization groups and p-adic analysis on stock markets. The problem is that I don't understand it yet. I need advice on the best path how to learn it. What I know already: - I've read most of Mac Lanes Algebra, so I know...

Hi- I've just completed problem 13.1 in Srednicki in which he tells us to relate the field-strength renormalization $Z_{\phi}$ to the spectral density $\rho(s)$ that appears in the Lehmann representation of the exact propagator. It seems straightforward-- I follow the hint, insert unity using...

I am trying to find out the density of electron positron pairs around a bare electron charge. In most texts, I saw that the treatment relates to the observed charge vs. the bare charge. I wanted to know if there is a formula that describes the density of electron positron pairs that surround...

Hello, I've been reading a book on QCD on I have a question: what is the purpose of the renormalization group? Is it to remove the large logs so that we can use pertubation theory (at least for large -q^2)? And what is the physical significance of the renormalization scale \mu^2?

Hello everyone. in standard approach to QFT, you study fields, S matrix, and you get a perturbative expression. You see that at higher terms you find infinities and so you renormalize. Now, Weinberg states that the renormalization procedure of mass and fields must be done even with no...

I have just read my first course on Quantum Field Theory (QFT) and have followed the book by Srednicki. I have peeked a bit in the books by Peskin & Schroeder and Ryder also but mostly Srednicki as this was the main course book. Now, I have to do a project in a topic not covered in the course...

Are there two separate renormalization group equations? One for how the physical coupling constants change with time, and one for how the bare parameters/coupling constants change with cutoff? Is there a relationship between the two? It just seems that textbooks use the term renormalization...

Remember that the electroweak force couldn't be renormalized for over many decades, until Weinberg and company finally renormalized it when mass was introduced via the higgs mechanism. Right? Now in the quantization of general relativity, we haven't been able to renormalize it after decades...

Renormalization Group concept is rarely given in laymen book on QM and QFT and even Quantum Gravity book like Lisa Randall Warped Passages. They mostly described about infinity minus infinity and left it from there. So if you were to write about QFT for Dummies. How would you share it such...

The following statements are from the paper with the above title, recommended in another thread, are from here: http://fds.oup.com/www.oup.co.uk/pdf/0-19-922719-5.pdf An interpretion of these statements would be appreciated: 1. [first paragraph, page 3] What is 'conservation of...

In Peskin- Schroeder, pag 412: "In massless phi4 theory, the one-loop propagator correction is completely canceled by mass counterterm." So, do massless theory provides mass counterterm? How is it generated? Maybe from a bare mass...don't have any clue. I'm confused because it seems that...

Hello everyone, I am currently studying the renorm. group in Stat. physics, more precisely how a rescaling (of space) leaves the partition function unchanged, at the price of having an infinite space of parameters due to the interaction proliferation at each rescaling. Let K be our...

Why do we care about Lorentz or gauge invariance if we're going to remove the cutoff at the end. our physical answers are independent of the procedure,, why do we care about preserving the symmetry "during" the calculation? Thanks for your time!

Hey, I'm just curious, MOND (Modified Newtonian Dynamics) seems to have a character of field renormalization where G is a running constant. Is there something to this relationship? Does anyone know of a review article that discusses this (or at least an article that someone in...

I encountered a paper in which the authors presented parton-level cross sections as a function of these variables: incoming particle momenta, factorization scale, renormalization scale, and strong coupling constant at the renormalization scale. I used to think that QCD factorization scale should...

I remember an argument which says that closed to critical points all systems are universal in the sense that their behavior is described by the critical exponents and that these critical exponents depend only on the dimension of the system and the dimension of the order parameter. I remember...

Hi everyone, even if I continue reading books about renormalization, I have the same basic doubts. So we have radiative corrections that give infinites etc.. So what we do is regularize and renormalize the theory. What is left at the end? Is it true that loops are no longer there since the...

Here and then I read gauge symmetry makes theories renormalizable. Unfortunately I could not find a satisfactory explanation why that so is. Could someone shed some light? thanks

Please teach me this: I think that renormalization problem happens in perturbative QFT,but not happens in nonperturbation theory.So I do not understand why renormalization problem appears in Quantum Gravity Theory despite of there are many nonperturbation theory to solve the problem? Thank you...

Please teach me this: Why the renormalization group flow and the fix-point depends only on the basic symmetry but not on the Lagrangian form.In general speaking,the physics laws depend only the basic symmetries?By the way,the Klein-Gordon,linear sigma,nonlinear sigma Lagrangian flow to one...

I found between my family's books (cousins mostly) 4 books for fluid mechanics, and since next semester i ll be taking it it d be cool if i could just chose between them. Oh btw its for mechanical engineering i currently have: Fluid Mechanics. Robert A. Granger...

I have a question about Fadeev-Popov (FP) ghosts. FP ghosts brake the gauge symmetry of the lagrangian and solve the problem of the divergence of the physical amplitudes, due to the gauge equivalence of the states. My question is: is it a renormalization process? I mean, the renormalization...

What I don't understand about WT identity is how it allows or helps you to renormalize a quantum field theory (es. QED). Not in details, just the basic ideas, if possible. Thanks in advice

Please teach me this: It seem to me that the objective of renormalization were the exclusion the infinities.But in renormalization group theory,they consider the dependence of physics parameters(e.g the interaction constant lamda,the mass parameter) on momentum p.Then I do not understand what...

Please teach me this: The parameters(mass,interaction constant) in classical Lagrangian can be freely changed in classical framwork,but how about in quantum framework?Then why we can freely arrange the renormalization conditions,because I think that we do not know whether the parameters can...

why can't gravity be renormalized?? i am just a novice in quantum physics...so i wud request to have an answer in a less technical way...

So far the spin foam renormalization programme has been very sparse. There's an old intriguing paper by Markopoulou that no one knows what to do with http://arxiv.org/abs/gr-qc/0203036 , and several recent papers from a group associated with Rivasseau http://arxiv.org/abs/0905.3772 ...

Can renormalization of QED really be interpreted as a dielectric shielding of the vacuum by electron/positron pairs that appear and disappear out of the vacuum? I understand that's what the Feynman diagram for the QED vertex suggests, since it's the internal fermion lines that interact with a...

Please teach me this: In renormalizable theory,a finite divergent constants being absorbed by counterterms diagrams which are straight line counterterms and vertex counterterms.But I do not understand why in higher order of perturbation series the absorption still work. Thank you very much in...

Hey folks, i have a question about LSZ and how to take into account the renormalization constants of the theory in question. In the derivation, only the field strength renormalization enters as a factor of Z (or square root thereof) but some mates said that also the vertex renormalization...

Hi all, I'm an amateur with some knowledge on the surface and actually am trying to make sense of the history of QM evolution and try to put things in place by trying to understand their 'raison d'être, at the time. So I'm back in: 1. 1926-28 with the question: how the introduction of...

I have a question concerning renormalization of QED. I don't know if Feynman diagrams with counterterms on ecternal legs are allowed. Normally to find S matrix amputated green function is necesary and to find it one don't take into account all propagators on external legs - they are canceled...

Hi, this is not based on detailed work but just an idea which arised comparing causal dynamical triangulations and loop quantum gravity. In CDT it seems reasonable to treat spacetime as a fractal. That means there is no limit or minimum length in the triangulations, but the triangulations...

how can logarithmic divergences be renormalized ? for example if i have \int_{0}^{\infty} \frac{log^{n}(x)dx}{x+a} differentiation with respect to 'a' and integration over 'x' gives finite result for example \int_{0}^{\infty} \frac{dx}{x+a}=-log(a)+C here 'C' would be an extra...

Can someone explain to me what renormalization is? And why General Relativity isn't renormalizable?

Hi, In \phi^4 theory, Srednicki deduces the self energy (equation 31.5), as: \Pi(k^2)=\frac{\lambda}{2(4\pi)^2)} \left[ \frac{2}{\epsilon}+1+ln\left(\frac{\mu}{m^2}\right)\right]m^2-Ak^2-Bm^2 I understand how he gets to this just fine, but now I'm trying to impose the usual on-shel...

What is it meant by "mass-independent renormalization scheme"? Does it mean that the counter-terms that cancel the infinities do not have dimensions of mass? In this case, any regularization scheme not involving the cutoff method, such as dimensional regularization? Or does it mean that...

The cutoff-method used for regulating divergences amounts to not integrating over field configurations that have a Fourier-momentum greater than the cutoff in the path integral. However, later on the cut-off is taken to infinity, so in fact we do integrate over all field configurations! The...

i would need some good books (with examples) in the following subjects - Feynman diagramas (how to calculate them) - Renormalization group my background: i have got a degree on physics, so i know what ODE , PDE , or even the Feynman integral and propagator, but i did not study the part...