Recent content by anthony2005

Thanks, that perfectly solved my problem. I wasn't thinking about the delta function carrying a dimension, but indeed if we think of \delta\left(\boldsymbol{p}\right)\propto\int d^{3}xe^{i\boldsymbol{p}\cdot\boldsymbol{x}} then the measure will lead to -3.

The pion decay constant f_{\pi} is defined by <0|\overline{d}\gamma^{0}\gamma^{5}u|\pi^{+}>=f_{\pi}m_{\pi} where I have set the momentum \boldsymbol{p}=0 (and used the temporal component of the axial vector). Now, at the right-hand-side the dimension is two (the decay constant and the mass are...

Hello, It's been a long time I am trying to accept renormalization in QFT but still I cannot be satisfied. The usual pedagogical way one introduces renormalization is to cure infinities that arise from perturbative expansions. Now, I can accept the statement that we are doing the perturbation...

First a little intro. The process of renormalization introduces in a QF theory a renormalization scale μ. Physical quantities do not depend on it, as a change of μ comes along with the change of the coupling g(μ) according to the RG law. But why then the physics can change so drastically...

So, is it correct to state in general that: "an integrable system is a system which thanks to certain properties its dynamics is exactly solvable" ?

The title is self-explanatory. What is it meant in the physics and maths community by the words integrability and integrable system?

Wow, it worked. Miracles are hidden in mathematica, but I'll figure out why it worked. Thanks a lot.

Hi all, I have a very simple issue, but can't get round of it. I have a long sum of rational functions, which is in the form for example \frac{n_{1}}{d_{1}}+\frac{n_{2}}{d_{1}}+\frac{n_{3}}{d_{1}}+\frac{n_{4}}{d_{1}}+\frac{n_{5}}{d_{2}}+\frac{n_{6}}{d_{2}}+\frac{n_{7}}{d_{1}\cdot...

Hi everyone, given a set of n+1 integers a_{1},a_{2},...a_{n},\rho , is it possible to get the closed form of the generating function f\left(x_{1},...x_{n}\right)=\sum_{i_{1},..i_{n}=0}^{\infty}\delta_{i_{1}a_{1}+...+i_{n}a_{n},\rho}x_{1}^{i_{1}}...x_{n}^{i_{n}} It seems to be always a...

Great, thank you very much!

Hello, how do you define a function or make a list with n elements, where n is any? More precisely there is a function in mathematica, BellY BellY[n,k,\{x_{1},...x_{n-k+1}\}] which gives the partial Bell polynomial. I would like to define in mathematica the complete Bell polynomial defined...

Hey, me again, maybe just those two conditions would give finite results at least in the UV, I've just realized that, for the \phi^{4} theory, mass and field renormalization induces the coupling renormalization since g_{b}\phi_{b}^{4} = g_{b}Z^{2}\phi^{4} =...

That is exactly what I was asking. But I don't think all correlation functions would be finite, since there is still the coupling renormalization missing (no \Delta\lambda counterterms). If they were finite and resolved all our problems I wouldn't know why Weinberg continued dealing with...

Ohhh thank you very much! I will read Srednicki, it seems pretty good. I definitely agree with you, I always find the sentence "In order to make this integral finite we introduce.." and I hate this way, I think it's not the way one should deal with physics. And after, they introduce the μ...

No answers? No need for detailed description, just a good reference is ok, i'll study from there..thanks