On Saturday, September 23, 2023 at 4:08:40=E2=80=AFPM UTC-5, Stefan Ram wrote:
I prefer to learn from books. But videos have two advantages: One
can watch/listen to them while doing household chores, and one also
learns the correct English pronunciation of the technical terms.
So I listened to some videos of QFT lectures by Prof. Susskind.
However, after about three videos so far, I am rather disappointed.
I have the impression that Susskind deliberately wants to
counteract all too flowery gobbledygook with a "don't talk, but
calculate" approach. I have always found such an approach absurd
in physics, but especially devastating in teaching. ...
Stefan,
I share your frustration and opinions. I've been trying to "understand"
QFT for almost 50 years now and still have some issues. Almost
everyone treats it as a math problem and it gets very abstract. After transforming to momentum space and doing a Wick rotation I'm not
sure what we are calculating anymore. I have some more fundamental
questions that may or may not be valid (I'm undecided on these):
-Transforming the path integrals to momentum space fundamentally
changes the integration. I'd have no issue with this in Newtonian
space-time, but the Fourier transform in Minkowski space-time does
not cover the same space-time volume as the spatial integration. My
real concern here is that the high momentum parts of the integration
is covering the same physical paths over and over again, and I
wonder if weighting the momentum integration proportionalto the
volume of space it represents might reduce the infinities calculated
and give a more reasonable result?
-I'm not sure how much this would affect the calculation of
macroscopic problems, as the wave function outside the light cone
is clearly attenuated, but for very small distances and very high
energies there is a bit of "fuzzyness" to the light cone, and I wonder
if that is part of the source of the infinities calculated particularly at higher energies and short distances.
-The Lagrangian used universally has F_{\mu\nu}F^{\mu\nu}, which
includes an electromagnetic field energy, which integrated over all
space gives an infinite result. This has been an embarrassment for
over 100 years now. I wonder (and this is by far an unconventional
opinion) if the concept of EM field energy is a mistake. It has been
known since at least the 1920's that if you do EM via potentials that
the energy of interaction has to be on the charges, not in the fields.
Wheeler and Feynman advocated for this briefly in the 1940's but
gave it up in light of the Lamb shift results. I wonder if maybe they
were too quick to give up on it?
Part of the problem is that QFT is necessarily a very advanced mathematical theory, and the people who can do the math easily are mathematicians.
But I'm a Physicist and I want to understand what the math is modeling,
and I'm often suspicious that mathematical transformations are changing
what is being modeled.
If you are inclined, I'd be interested in discussing issues and ideas, and
I'll try not to bother you too much with my heretical thoughts. We might
be able to help each other.
Rich L.
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