Renormalization Definition and 184 Threads

There are several reasons given in the literature, why UV infinities arise in QFT in the first place. My problem is putting them together, i.e. understand how they are related to each other. So... UV divergences arise and thus we need to renormalize, because: We have infinite number of...

Hi all, I have doubts on the role of the Field Strength renormalization ##Z_\psi=1+\delta_\psi## when computing amplitudes. I never did this, maybe because it was not needed before, but i noticed that in the solution of a specific problem, to obtain the correct result, you need to multiply the...

I see re normalization being discussed in many situations and it is not very clear what unites them. For example it is talked about during self energy, then when integrals are blown by high energy(in scattering problems I presume), or some problem with IR(the opposite). Then there are these...

I am aware of only two fields where the renormalization (sub)group ideas can be systematically and unambiguously applied: particle physics and equilibrium critical behaviour. 1.- Are there any others? 2.- What are these ideas used for in fluid mechanics? 3.- When cosmologists speak about...

I am trying to understand the basics of Renormalization. I have read that β encodes the running coupling and can be expanded as a power series as: β(g) = ∂g/(∂ln(μ)) = β0g3 + β1g5 + ... However, I don't understand how this is derived.. I assume that the terms correspond to 1 loop, 2 loops...

Hi everyone, Currently, I am self-learning Renormalization and its application to PDEs, nonequilibrium statistical mechanics and also condensed matter. One particularly problem I face is on the conservation of symmetry of hamiltonian during renormalization. Normally renormalization of...

I've been trying to get a rough understanding of what renormalization involves (in a particle physics context; I'm aware it has many other applications eg. condensed matter) but it hasn't quite clicked yet. The things I have in my head so far are as follows: - A particle will be surrounded by a...

Hi everyone, i'm not able to find the exact definition of mass independent renormalization scheme. I often read that the MS-bar scheme is mass independent, but why? And why this feature help us to compute the beta function? Thanks in advance, Luca

The pole masses of the heavy quarks (c, b and t) are relatively well defined in QCD (i.e. the solution of m²(p²) = p² extrapolated using the beta function and the available data from other values of µ usually obtained based upon model dependent decompositions of hadron masses that include these...

Is the one-loop corrected vacuum expectation value of a field renormalization scheme independent?

I'm currently studying the Landau-Wilson model for critical phenomena (Statistical Mechanics, Kerson Huang) where the renormalization group is a central object. In the end, the calculations lead to a set of coupled differential equations that describe the (metaphorical) evolution of the...

Hello all, I hope you can give me a hand with a QFT homework I'm working on. We are to compute the beta equation of a Non-abelian SU(N) theory with: Complex scalars (massless), bosons, ghosts. My question is referring to the Boson self-energy scalar loop correction. 1. Homework Statement We...

The Electron Rest Mass is considered as a fundamental constant of nature. In relativistic Quantum Field Theory, in contrast, divergences arise. In order to deal with these divergences, one uses renormalization. According to this renormalization, the 'macroscopic' parameters of the lagrangian...

Given a Yukawa coupling as a function of scale and a vev, how can I compute the corresponding pole mas? Understandably most paper explain how from a measured pole mass one can compute the running mass, for example, Eq. 19 here. However I want to compute the pole mass from the running mass. In...

Does it make sense to talk about the top mass at energies below mt, although in all processes the corresponding energy scale is above mt because of the rest mass energy of the top quark? Using an effective field theory approach, the top quark decouples at energies below the top quark mass and...

Hi, I am about to work on the problem of trying to find a renormalization program for bound states in QFT. Any suggestions/advice on where to start would be much appreciated.

I have read many times that a theory (such as gravity) that contains couplings with negative mass dimensions cannot be asymptotically free. Does anyone have a reference that proves that that's the case? The argument is usually just that the coupling grows with energy, as seen in the...

Possibly very silly question in QFT. Consider the Lagrangian for a scalar field theory. A term like g/φ^2 should be renormalizable on power counting arguments. The mass dimension of g should be 2 (D-1) where D is the number of space-time dimensions.Does this make sense?

A question that has been bothering me for a while, is why are we as a physics community so fine with remormalization in QFT? Experimentally (QED especially) the field is VERY precise, however, looking at the mathematical side of renormalization, it doesn't look... very logical. We get divergent...

Which books in QFT give representations about general proof of renormalization?I know that the book of QFT of Peskin&Schroder does not give the full demontration.

On page 164-165 of srednicki's printed version (chapter 27) on other renormalization schemes, he arrives at the equation $$m_{ph}^{2} = m^2 \left [1 \left ( +\frac{5}{12}\alpha(ln \frac{\mu^2}{m^2}) +c' \right ) + O(\alpha^2)\right]$$ But after taking a log and dividing by 2 he arrives at...

Does anyone know any good references for discussion of ##\overline{MS}## theory in phi^4 theory?

I guess my question is pretty basic, and following a procedure in the textbook by Lahiri and Pal. You can see the relevant pages at https://books.google.com/books?id=_UmPP8Yr5mYC&pg=PA245&source=gbs_toc_r&cad=4#v=onepage&q&f=false On eqs. (12.84)-(12.86). I don't see how to get from (12.85) to...

Hello Everybody, I am searching for a book that introduces the theory of renormalization other then Peskin Schroeder, I found Peskin Schroeder cumbersome regarding this topic. Can anyone help? Thanks in advance!

It's non-trivial since if you do not have a background metric you cannot define the scale, with respect to which couplings are supposed to run. So new approaches to renormalization have appeared. Perimeter has a workshop on this and a number of Monday 28 Sep talks are on line...

Hi all -- can anyone offer a qualitative explanation of why it is that couplings run with the energy in *relativistic* quantum theory, and not in non-relativistic? Some insight here would be much appreciated. Thanks.

Hi, I'm confused about the discussion on p28 of Nigel Goldenfeld's "Lectures on phase transitions and the renormalization group" (this question can only be answered by people who have access to the book.) The goal is to compute the potential energy of a uniformly charged sphere where the...

In the canonical formulation of QFT (to which I've been exposed), it is always argued that only differences in energy are physically observable and so we can deal with the fact that the vacuum energy is infinite by redefining the vacuum such that its energy is zero and we subsequently measure...

I think I have found a mistake/wrong formulation at Peskin’s, when he discusses the renormalization of QED. In particular, he defines the 1PI of the electron’s self-energy on page 331 as: –i\Sigma( \displaystyle{\not}p ) and the corresponding counterterm on page 332 as: i(...

According to Peskin, p.414, at the bottom, as part of calculating the ##\beta## functions of a theory, we need to fix the counter terms by setting the "typical invariants" built from the external leg momenta to be of order ##−M^2##. For a 4-point function, these invariants are s, t and u...

I am trying to calculate the ##\beta## functions of the massless pseudoscalar Yukawa theory, following Peskin & Schroeder, chapter 12.2. The Lagrangian is ##{L}=\frac{1}{2}(\partial_\mu \phi)^2-\frac{\lambda}{4!}\phi^4+\bar{\psi}(i\gamma^\mu \partial_\mu)\psi-ig\bar{\psi}\gamma^5\psi\phi.##...

i am really confused about it.i know this much that it is used to cancel out the infinities to combine the theory of relativity and quantum physics.i just want to know how.and also what is super symmetry?please help.

The question is in the title: is it possible for a theory to be both UV and IR stable? And concrete models would be much appreciated!

The problem statement. When an exercises say " the interaction in a QFT has dimensions Δ" , what does it mean?, it means the field or the Lagrangian has this mass dimension? In this exercise I'm trying to find the classical beta function (β-function) for the assciated couling.

as a new proposal for QGhttp://arxiv.org/abs/1502.05385 Tensor network renormalization yields the multi-scale entanglement renormalization ansatz Glen Evenbly, Guifre Vidal (Submitted on 18 Feb 2015) We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of...

I have a couple of questions regarding renormalization. 1. If it is possible to change mass as long as we do it simultaneously with changing ultraviolet cutoff, that would imply that the value we pick for mass is more or less arbitrary. If so, how come we have exact decimal value of mass of an...

I was trying to learn renormalization in the context of ChPT using momentum-space cut-off regularization procedure at one-loop order using order of p^2 Lagrangian. So, 1. There are counter terms in ChPT of order of p^4 when calculating in one-loop order using Lagrangian of order p^2 . 2...

I am currently studying QFT with 'An Introduction to Quantum Field Theory' by peskin. In part 2 (renormalization) of the book, he introduces counterterms and shows how to compute scattering amplitude with them. Below are counterterms of \phi^4 theory: Then he calculates a 2-2 scattering process...

Why density matrix renormalization group theory works only for 1D systems?

I'm studying renormalization and I have a question about part of a textbook. In P&S at the top of p.324 they show the divergent amplitudes of phi^4 theory, and they say that the two-point vertex (which has superficial degree of divergence D=2 according to the formula they derive) will have a...

Hi all. Consider a UV cutoff regulator ##\Lambda## with an effective QED lagrangian ##\mathcal{L}_{\Lambda} = \bar{\psi}_{\Lambda}(i\not \partial - m_{\Lambda})\psi_{\Lambda} - \frac{1}{4}(F^{\mu\nu}_{\Lambda})^2 - e_{\Lambda}\bar{\psi}_{\Lambda}\not A_{\Lambda}\psi_{\Lambda}##. One can of...

This is a ambarassingly simple question, the question is if my explantion is acceptable. I have come across the integrant form negative infinity to positive infinity and I have come across the integrand from 2pi to zero that is set equal to 1 and then abs value squared of the wavefunction and so...

Hi all! I'm a beginner in QFT. I've read a lot of posts here about Haag's theorem, but I haven't found one which can answer simply and briefly to my question (if such an answer exists): Do UV divergencies appear because of the Haag's theorem? Thank you

Since Wilson work in the 70s, the renormalization technique in QFT is physically justified with the concept of scale dependence(scale anomaly) of the parameters. This apparently is akin to a universal version of the characteristic length usually applied to specific physical systems to define...

Suppose you have λø4 theory and calculate the bare 4-point function: $$ \Gamma_0(s,t,u)=\lambda_0+\lambda_0^2f(s,t,u)\\ =\left[\lambda_0+\lambda_0^2f(0,0,0)\right]+\lambda_0^2\left[f(s,t,u)-f(0,0,0)\right] $$ We then take a measurement at (s,t,u)=(0,0,0) and call the result λR. Then $$...

I have some questions about this paper:http://users.phys.psu.edu/~radu/extra_strings/freedman_sigma_model.pdf In section 3, they renormalize the bosonic non-linear \sigma model at one loop level. The action is given by I_B[\phi]=\frac{1}{2}\int...

Hi guys. I'm working on a model described by a non-local QFT. I think I got the Feynman rules right, but I get divergences from ##\delta(0)##-like factors.Homework Statement It's a QFT for a complex scalar field ##\psi(x)=\psi(\mathbf{x},t)## with action $$S= \int dx...

What type of group is the Renormalization Group? All I've seen is people giving a (differential) equation for beta-function when they teach for the RG... Also I haven't been able to find an algebra characterizing the RG... Any clues?

Perimeter conference http://pirsa.org/C14020 Here are links to the talks' videos and slides PDF Recent developments in asymptotic safety: tests and properties Tim Morris http://pirsa.org/14040085/ What you always wanted to know about CDT, but did not have time to...

Freidel "Continuum Limit and Renormalization" ILQGS 1/4/14 http://relativity.phys.lsu.edu/ilqgs/ Tomorrow Laurent Freidel gives the online International LQG Seminar talk, the topic being "Continuum Limit and Renormalization". It might be helpful to look over a Freidel paper ahead of time...