Youtube introductions to quantum field theory

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#2
confused2 Offline
I'm not a physicist but..
For the purposes of discussion I'm going to comment. Mostly I'm completely lost so any help would be appreciated. I'm mostly quoting from the video so not explicitly using quotation marks.

The fields seem to be dictated by symmetry (rotation, displacement and change of frame of reference). Where there is a symmetry there is a field and where there is a field there is (potentially) a particle. A banana doesn't look the same as you rotate it so it would seem there won't be a banana field. But.. looking at particles with spin which have to be rotated through 360 degrees to get back where you started .. from memory these things come with either spin up or spin down so they don't rotate nicely.
For example the Stern-Gerlach experiment (best with electrons)
https://en.m.wikipedia.org/wiki/Stern%E2...experiment
Maybe this will become clearer in another video.

Further requirements of these fields are:
Conservation of energy,momentum, angular momentum and velocity of the centre of mass - all this with a quantum 'particle' that seems (?) spread out in space or something (?).

Jumping ahead a bit.. the electrostatic field of an electron isn't so much generated by the electron but more the electron disturbs a field that is already there. The electric field has symmetry so spontaneously exists without us having to ask for it. ???

Moving to quantum fields - they are quantised and can only contain an integer number of disturbances.
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#3
C C Offline
Since the same suspects will appear in anyone's dragnet, there doesn't seem much point to my adding more "Introduction to QFT" videos. So...

TANGENT: (3) A topic nearly unrelated to the main topic, but having a point in common with it.

- - - - - -

2 to 3-minute trailer video for below: The Bridge Between Math and Quantum Field Theory

Nathan Seiberg on how math might complete the ultimate physics theory
https://www.quantamagazine.org/nathan-se...-20210624/

EXCERPT: You’ve also mentioned that it’s a sign of incompleteness that QFT doesn’t have its own place in mathematics. What does that mean?

We cannot yet formulate QFT in a rigorous way that would make mathematicians perfectly happy. In special cases we can, but in general we cannot. In all the other theories in physics — in classical physics, in quantum mechanics — there is no such problem. Mathematicians have a rigorous description of it. They can prove theorems and make deep advances. That’s not yet the case in quantum field theory.

I should emphasize that we do not look for rigor for the sake of rigor. That’s not our goal. But I think that the fact that we don’t yet have a rigorous description of it, the fact that mathematicians are not yet comfortable with it, is a clear reflection of the fact that we don’t yet fully understand what we’re doing.

If we do have a rigorous description of QFT, it will give us new, deeper insights into the structure of the theory. It will give us new tools to perform calculations, and it will uncover new phenomena.
Are we even close to doing this?


Whatever approach we take, we get stuck somewhere. One approach that gets close to being rigorous is we imagine space as a lattice of points. Then we take the limit as the points approach each other and space becomes continuous. We describe space as a lattice, and as long as we’re on the lattice there is nothing non-rigorous about it. The challenge is to prove that the limit exists as the distance [between points on the lattice] becomes small and the number of points [on the lattice] becomes large. We assume this limit exists, but we cannot prove it.

So if we do it, will a rigorous understanding of quantum field theory actually merge it with general relativity? That is, will it provide a long-sought theory of quantum gravity?

It’s quite clear to me that there is one intellectual structure that includes everything. I think of quantum field theory as being the language of physics, simply because it already appears like the language of many different phenomena in many different fields. I expect it to encompass also quantum gravity. In fact, in special circumstances, quantum gravity is described by quantum field theory.

It might take a century or two, even three centuries, to get there. But I personally don’t think it will take that long. This is not to say that in 200-300 years science will be over. There will still be many interesting questions to address. But with a better understanding of quantum field theory, I think [discovery] will be a lot faster.
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