Renormalization Definition and 184 Threads

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...

Hi all, I have two questions regarding chapter 27 and 28 in Srednicki's book. On page 163 he states: But this would mean that |<k|\phi |0>|^2 = R I can not see why this is? I would expect that the result is R^2 because there is a factor of k^2 + m^2 in the LRZ formula... My second...

hellow everybody i have a problem in styding the critical bihaviour of the tow dimensional ising model when i use periodiques boundary conditions i found that the fixed point for this case is the PRG equation that mean the following recursion relation...

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...

Dear experts, Does renormalization mean discarding corrections to a known constant? I mean, we assign a known value to the electron mass or charge, whatever, in the zeroth order of the perturbation theory, for example, in QED. In the next order we obtain a correction to this value (finite...

Does Renormalization group tell you if a theory is Renormalizable or not ?? the idea is this, using the Renormalization group equation for our theory (QED, Gravity, Gauge theories..) can tell this RG equation if our theory is renormalizable or not for big or small energies ??

Hello, in our lecture, we computed \beta^{\overline{MS}} , \gamma_m^{\overline{MS}} for - \frac{\lambda}{4!} \phi^4 Theory. These are: \beta^{\overline{MS}} (\lambda_{\overline{MS}}) = b_1 \lambda_{\overline{MS}}^2 + O(\lambda_{\overline{MS}}^3) \gamma_m^{\overline{MS}}...

Hello, to understand the renormalization of phi^4 theory, I read Peskin Schröder and Ryder. In both books important steps are left out. I found the following identity in Peskin Schöder "An Introduction to Quantum Field Theory" on page page 808, equation A.52 (Appendix) \frac{\Gamma(2 -...

Hello, I read chapter 7.1 of "An Introduction to Quantum Field Theory" by Peskin and Schröder and have two questions. They derive the two point function for the interacting case. On page 213 they manipulate the matrix element, after insertion of the complete set of eigenstates. <\Omega...

I'm just learning renormalization in QFT and have a few basic questions: 1) It seems to me that renormalization has the status of a *prescription* for extracting a finite number from an infinite one. It cannot be justified except that this prescription leads to agreement with experiment. Is...

I have a question about the MS renormalization scheme. When you choose this scheme, all sorts of strange things start happening. The mass in your Lagrangian can no longer be the physical mass. The 4-momentum of a physical particle squares to the physical mass, not the free-field mass. But what I...

My (weak) understanding of renormalization is that following regularization, the divergent terms coming from loop integrals can be canceled by adding counterterms to the Lagrangian which are of the same form as the original terms. What does this mean in terms of actual calculations? Does it...

During a lecture about QFT (http://video.google.it/videoplay?docid=-8230150359736309141&ei=xFWDSNSiDITgjAKz46i3Bg&hl=it" ) Alain Connes said that Green (in1850) used a mass renormalization to calculate the acceleration of a ball in a liquid, because you can't directly calculate it just using...

Feynman refers to "renormalization" as a dippy process on p.128 of his book "QED - The Strange Theory of Light and Matter". His words are: "The shell game that we play to find n and j is technically called renormalization. But no matter how clever the word, it is what I would call a dippy...

What is the idea behind renormalization group ?? i believe you begin with an action S[\phi] =\int d^{4}x L(\phi , \partial _{\mu} \phi ) then you expand the fields into its Fourier components upto a propagator.. \phi (x) =C \int_{ \Lambda}d^{4}x e^{i \vec p \vec x} + c.c but...

When we compute scattering amplitude \mathcal{M}, using a coupling constant \lambda, and a cut-off energy \Lambda, it turns out that if \lambda is constant, then \mathcal{M}\to\infty when \Lambda\to\infty. The idea of renormalization seems to be, that we relate some physical coupling constant...

what is renormalization really and what does it do?

Hi.. in what sense do you intrdouce the cut-off inside the action \int_{|p| \le \Lambda} \mathcal L (\phi, \partial _{\mu} \phi ) then all the quantities mass m(\Lambda) charge q(\Lambda) and Green function (every order 'n') G(x,x',\Lambda) will depend on the value of cut-off...

If the problem of renormalization is that there are divergent integrals for x-->oo couldn't we make the change. \int_{0}^{\infty}dx f(x) \approx \sum_{n=0}^{\infty}f(nj) using rectangles with base 'j' small , and approximating the divergent integral by a divergent series and 'summing' by...

Renormalization differential equation ?? Let's suppose we have in perturbation theory the quantities (m_0 , q_0 , G_0 (x,s)) With m,q, and G(x,s) the 'mass' 'charge' and 'Green function' (propagator) and the sub-index '0' here stands for "free" theory (no interactions) Then my...

Hi everyone! I have a few questions regarding renormalization in QFT. 1. In Peskin chapter 10, he renormalizes \phi^4 theory using the renormalization conditions in equation (10.19), which basically say that the propagator has a pole at p^2=m^2 and that the 4-point interaction is exact for...

Check the webpage.. http://arxiv.org/ftp/math/papers/0402/0402259.pdf specially the part of Abel-Plana formula as a renormalization tool... \zeta(-m,\beta)-\beta ^{m}/2- i\int_{0}^{\infty}dt[ (it+\beta )^{m}-(-it+\beta )^{m}](e^{2 \pi t}-1)^{-1}=\int_{0}^{\infty}dpp^{m} valid for...

In modify minimal subtract sheme,using dimension regulation, I calculate the the renormalization constant of massive quark and massless quark,get the same result.But in some papers,they are different. Is there a review or any book on MS renormalization,that giving all the self energy and...

Imagine the vertex correction diagram in the pseudo-scalar meson theory. The amplitude for this diagram is UV divergent. In order to get rid of this divergence we apply regularization technique and obtain the expression with the UV cut-off parameter. The usual practice is that we expand the...

Dear PF, Would you please help me with one question? I have put my question in attachment, because latex does no generate formulas (I don't know why, but previously it did). Thanks. George

When was reading about renormalization I did no understand the main Idea of the last :(:confused: It has been considered photon propagator with virtual pair of electron/pozitron. Takeing that loop integral the M^2 cuttoff is introduced, which tends then to ininifity, M^2 is "sopped up" in...

renormalization and divergences... let suppose we have a formula for the mass in the form: m=\int_{0}^{\infty}dxf(x)e^{-ax} a=ln\epsilon with epsilon tending to zero so a is divergent..but if we perform the integral numerically: m=\sum_{j}w(x_{j})c_{j}f(x_{j})e^{-ax_{j}) so we...

for a divergent series i can write an expression in the form: \int_{R}dxC(x)w(x)e^{-ax} where a is a divegent quantity in the form a=ln\epsilon the qeustion is how i would apply renormalization?..in fact if we apply functional differentiation respect to e^{-ax} we get C(x)w(x) the...

How much is this renormalization business a problem in QFT? Always read it’s complete ‘hand-waving’ and arbitrary, but also that QFT is the most precise theory ever. Also found this quote: "[Renormalization is] just a stop-gap procedure. There must be some fundamental change in our ideas...

I would like to know what is callan-symanzik equation used for in renormalization theory , if this can give you the renormalizated quantities and why can not be used when the theory is non-renormalizable.

When i coursed the quantum field theory at university our teacher told us about this equation..i have searched information aobut it in many books and have the form...it seems is a partial-differential equation but i have doubts.. a)what is have to do with renormalization?...(in fact how to...

Where could i find a good introductionto renormalization theory ? ( i have a degree in physics but i do not know about renormalization). In fact i have some questions: Let us suppose we have the series: f(g)=a0+a1g+a2g**2+.. where g is the coupling constant and a0,a1,a2,a3..an are numerical...

Canonical Transformation and renormalization... Let be L a lagrangian of a Non-Renormalizable theory..then we could take its hamiltonian. Then after taking Hamiltonian you could take a Canonical Transformation to find another (renormalizable) Hamiltonian..and solve it..¿why this trick is...