1. Jan 13, 2006

### Sombrero

When was reading about renormalization I did no understand the main Idea of the last :(
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 renormalized coupling constant, but even then when M^2 tends to infinity the coupling constant runs to infinity? Yes? Am I clear?

Pls help

2. Jan 13, 2006

### Sombrero

3. Jan 16, 2006

### Sombrero

Gents,
I am not familiar with physics and that's why my questions may seem stupid for you, but could you pls help me and explain the Idea of formula 7.27 in attached file from Halzen F., Martin A.D. Quarks and leptons.
Does not the e_R tends to infinity when M^2 goes to infinity?
Thank you very much.

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4. Jan 16, 2006

### vanesch

Staff Emeritus
???

5. Jan 16, 2006

### George Jones

Staff Emeritus
My feelings exactly!

Regards,
George

6. Jan 16, 2006

### Norman

Sorry, in my sickly, feverish state I didn't elaborate. He is asking about how Halzen and Martin go about doing renormalization of the electric charge. They introduce the cut-off, M, and show that the renormalized charge goes like:
$$e_r \approx e(1-Log[M^2])^{\frac{1}{2}}$$
With a bunch of stuff I cannot remember off hand. So my understanding of the question was basically a simple math question. What does the limit as M-> infty do to e_r.
Did I misinterperet or just not state enough in my original post? Maybe my math is completely wrong, that tends to happen with a fever...

Last edited: Jan 16, 2006
7. Jan 16, 2006

### Perturbation

The limit of log(x²) as x->infin isn't zero.

8. Jan 16, 2006

### gulsen

isn't it $$2 \log x$$ and $$\log x$$ approaches to infinity at $$x->\infty$$?

9. Jan 16, 2006

### Norman

OMG...:rofl: :rofl:
Well, the good news is I am feeling better and now see where I went wrong... I even checked it with mathematica, funny thing is if you switch the variable and the base in mathematica, you get a very different answer...

time to get some rest... I suppose this means all the work I did today needs to be rechecked.

Edit: I deleted the post- my shame is too deep...

Last edited: Jan 16, 2006