Oh, I am sure
Wo is curious to know how I managed to write my
last posting, since at that time
he was sitting at my computer while I was hanging around on my bed, 2 meters away.
Well, it's just that my computers clock used to be
3 minutes late.
Wenn das nix wird mit der Physik, dann entwickle ich eine Schuhsohle mit Hundescheisse Antihaftbeschichtung, damit kann man in dieser Stadt Millionaer werden.
I have definitely a conceptual problem with renormalization in
quantum field theory. That has been intriguing me for
a couple of weeks now. But until now I haven't come farther than discovering
what it is, that I don't understand:
If you draw Feynman graphs of, say, vertex corrections and calculate them
your integrals diverge. That's easy to see, just write them down and
there it stands. I do also accept that you need all this vertex corrections,
self-energy terms etc., since you can measure their effects
(i.e. anomolous magnetic moment of the e-, Lamb shift in QED, etc).
So, as far as I have understood it, you claim that your physical quantities,
such as coupling constants, masses etc. must be finite.
That's certainly very plausible.
That's therefore a kind of boundary condition in your calculation.
Now you separate
the divergencies in your loop integrals through an appropriate regularization
and define them away in nur renormalized quantities. Fine.
But, why do these infinite terms appear in the first place?
Is this just a formal problem, i.e. the technical procedure you use for
your calculation isn't really adequate, that means some very clever physicist
could invent a new calculation method which would do away with all
these divergencies.
Or is there more about it? Do the divergent terms have a physical meaning?
And if they have, what is it? Do they arise because you truncate your
expansion series? That would mean that your series has a very lousy convergence
behaviour. And wouldn't this just cast doubt on a perturbational treatment?
But maybe this is just what one does, since one knows a priori
that the series converges, no matter how (because of the boundary condition mentioned above).
Anyhow, if I just naively write down my Lagrangian, and
determine the elements
of the S-Matrix of my theory, I have the bare coupling in
my Lagrangian.
I therefore expand around the bare coupling which might turn out
to be infinite. That wouldn't be a proper set up for perturbation theory, would it?
Well, if it is the case that the infinities are due to the truncated
version of an infinite series, then of course the renormalized coupling
turns out to be identical to the bare one in the limes to infinity and
the expansion parameter is small nevertheless.
I do not post that often on physics. And normally if I read these postings
again after a certain time, I must admit, that they were based on
misunderstandings. That's good because you notice, that you have
learned something, although it is a little bit embarrassing to
have such
postings in
your weblog.
Unfortunately I never have
NASA-Spam in my mailbox.
Oh yes, I definitely want one of these "Fleckerlteppich".
I wanted to update the surroundings of my weblog for a long time,
well I finally added some more weblogs I occasionally read.
Although I am not a very frequent weblog reader neither.
Most of them
are physics blogs. You might even learn something on string theory
there,
I don't understand it normally.
And
Sean Caroll is the guy with the very famous
lecture notes on GTR.
Just have a look at the side bar.
I hope to do some more updating sooner or later.
Anyway, as you can see I am taking
some of my postings very seriously. I don't believe that I will get more readers if I write in English, but I take it as an exercise.
There hasn't been a lot of blogging in the last weeks, and un fortunately it won't ameliorate. At least I fixed the link
in my last posting Well, I am not sure wether it is the article I wanted to
link to in the first place.
