Regularization Definition and 71 Threads

I was looking at a paper that used dimensional regularization and the following expression was derived: \int dx \mbox{ }[p^2(1-x)^2-\lambda^2(1-x)]^{\epsilon} Factoring out p^2(1-x)^2 : \int dx \mbox{ }[p^2(1-x)^2]^{\epsilon}[1-\frac{\lambda^2}{p^2(1-x)}]^{\epsilon} The part that I...

Hi folks - I have a couple of questions about EFTs that are driving me crazy. (1 ) Consider first of all a Wilsonian effective Lagrangian - one in which particles of mass >M have been integrated out from a 'full' Lagrangian leaving a string of non-renormalizable interactions amongst the...

can zeta regularization provide FINITENESS to quantum field theory ?? recently i came across (google) these papers http://vixra.org/abs/1003.0235 http://vixra.org/abs/1001.0042 http://vixra.org/abs/1001.0039 using the zeta regularization algorithm plus analytic continuation he...

why does dimensional regularization need counterterms ?? if all the integrals in 'dimensional regularization' are FINITE why do we need counterterms ?? in fact all the poles of the Gamma function are simple hence the only divergent quantity is the limit as d tends to 4 of 1/(d-4) which is...

how does this regularization work ?, suppose we have three kinds of divergencies \Lambda ,.. log \Lambda and \Lambda^{2} then according to Pauli-Villars regularization should we add 3 different and ficticious 'Fields' with Masses A,B,C tending to infinity ??

Hi guys, this is my first post. I recently realized that there is something odd going on with dimensional regularization so I figured I could ask here. So let's take equation (A.44) in Peskin's book. Now if we set n=1 and d=3-e, this integral is obviously ultraviolet diverging(in fact...

Zeta regularization for UV divergences ?? I know that zeta regularization makes sense but is this paper correct ? http://arxiv.org/ftp/arxiv/papers/0906/0906.2418.pdf watched on arxiv by a chance, there are 2 sections the 'divergent integral' treatment by using zeta regularization is on...

i have been reading several introductory papers to 'dimensional regularization' they tell how it can be applied to QED and so on, but the problem is why this dimensional regularization technique can not be applied to get finite answer in Quantum Gravity ??

Is "Zeta regularization" real?? in many pages of the web i have found the intringuing result \sum _{n=0}^{\infty} n^{s}= \zeta (-s) but the first series on the left is divergent ¡¡¡ for s >0 at least other webpages use even more weird results \sum _{n=0}^{\infty} h^{s+1}(a/h +...

What is the best automated way to select the regularization parameter in a Tikhonov regularization? Can you point me toward some code for this purpose? Thank you,

although is not valid in general (since an Euler product usually converges only when Re(s) >1) \frac{ d \zeta(1/2)}{\zeta (1/2)}= -\sum_{p} log(p)(1-p^{1/2}

how does dimensional regularization work ? i see , how can you calculate integrals in d-dimensions of the form \int d^{d} k F( \vec k ) ?? and for other cases , let us suppose we have the integral \lim_{\varepsilon\rightarrow 0^+}\int \frac{dp}{(2\pi)^{4-\varepsilon}}...

I read that for the divergent series: 1+2+3+...=-\frac{1}{12} It was said that is obtained by using the so called regularization technique (zeta function regularization?). I would like to see an explicit proof for that. Can anybody suggest a suitable source where this can be found?

Does a http://en.wikipedia.org/wiki/Tikhonov_regularization" solution for least squares have to be iteratively solved? Or is there a way to perform regularization via linear algebra, the way linear regression can be done by solving the (XTX)B=XTy normal equations?

Hi guys, I want to learn about Dimensional Regularization for the electron self energy. Can you help by providing me the best book or notes for this purpose”it's a self study”? Thanks for you help.

Hi! I want to renormalize the following UV-divergent integral using Dimensional Regularization: \int_{- \infty}^{\infty} \frac{d^4 p}{\left(2 \pi \right)^4} \frac{1}{a p_0^2 +\left(a p_x^2+a p_y^2+a p_z^2 +M^2\right)^2} a>0 I can only find literature which deals with integrands...

surfing the web and arxiv i found the strange formula lnA= \frac{d^{n}}{ds^{n}} \frac{s^{n-1}}{n! A^{s}} my question is .. where does this formula come from ?? here 'n' is supposed to be a finite parameter we must define to avoid the divergences, is it valid for non-renormalizable or...

Hey folks, I've been stuck on this for two days now so I'm hoping for some hints from anyone... I'm trying to show: -\frac{1}{2}\int\frac{d^{2n}k}{(2\pi)^{2n}}\frac{1}{\Gamma(s)}\sum_{m=-\infty}^{m=\infty}\int_0^\infty...

...on the off chance anyone knows this, I'm trying to get from: V=\frac{1}{2A}Tr Log(\frac{-\Box}{\mu^2}) to V=\frac{(-1)^{\eta-1}}{4\pi^\eta\eta!}\frac{\pi}{L}^{D-1}\zeta'(1-D) I know this is a shot in the dark, but in case anyone has experience. The paper I'm reading explains...

i'm doing an integral for my advisor that is way beyond me but i have pages from a textbook that tell me how to do it so here goes \int\frac{d^4\ell}{(2\pi)^4}\frac{1}{(\ell^2+A^2)^2} = \frac{1}{2}B(0,2) which is divergent but in arbitrary dimensions you get...

I'm working with a hypersingular boundary integral equation and its numerical implementation (the traction (dual) boundary element method equation). This involves numerical evaluation of a Hadamard integral and I'm collecting whatever material I can find about the regularization method itself...