[ShinyRice]

I don't understand why you're getting snagged up on in QFT, I've recently done a course on that and it wasn't that complicated, though that's if and only if you've studied or at least understood the algebra of creation and destruction operators found in the quantum harmonic oscillator, and classical field theory. I didn't have a course on classical field theory, but I did have a chapter of a course dedicated to it.

In terms of math, I've only encountered linear algebra, multivariable calculus with A LOT of Dirac deltas and a smidge of complex analysis, necessary to calculate the Feynman propagator.

[jiggawatts]

My problem with QED/QFT is that it gets about five levels of abstraction too far from physical intuition and then really starts layering on the algebra. At the end, it's totally abstract and I very strongly suspect (but cannot prove) that nobody knows what it all means in the end.

My current pet project is to try and write a "renderer" that uses QED, or better yet, some more advanced subset of the Standard Model instead of the oversimplified "raycasting" model typically used in computer graphics. I'd be happy with a "quantum" Cornell Box, ideally in a fully relativistic model that can simulate the speed of light, diffraction, interference, etc...

I'm trying to see how far modern physics has gone and still be in contact with a fully general, numerical, real theory. Not just the abstract properties of statistical theories, if you know what I mean.

So far it hasn't been a fruitful journey, I can't even find a reasonable description of an electron's U(1) field equation as described by QED. I get that it has a bunch of properties such as its symmetries, transformations, etc... but this is like the description of an elephant by a blind man touching each part.

[abecedarius]

That would be a marvelous project to see.

I've wondered something myself ever since since reading Feynman's popular book QED. That book is clear and illuminating, no question, but in the end it doesn't quite deliver an understanding that I could program. Of course I could code up his explanations of reflection and diffraction, and so on. But there's a gap between those and what he was proposing to show us: a grasp of what the theory calculates, leaving out all the fancy techniques needed for practical calculations. If I'd gotten that, I would be able to code QED, setting aside all efficiency and numerical stability. To get there, if I try to bridge the gap from other sources it looks like years of work, because none of those sources reach anywhere near this end of the chasm. Why not attempt a "QED for programmers" as a literate program or explorable explanation? Maybe I will someday, but I have a lot of sloth to overcome. Good luck (and if you ever feel like chatting more, feel free to bug me).

[yummypaint]

I reccommend also doing some reading about foundational lattice field theory concepts in parallel with classic QFT. Comparing and contrasting the two can help with understanding both. Maybe start with ultraviolet divergence? Lattice based theories have also been more successful as far as making good predictions. I think it appeals to intuition that people who write software may find more familiar.

[jiggawatts]

I've looked, but generally I found that lattice models:

1) Have dramatic simplifications, such as 2D models.

2) Use made-up physical constants to make the computations tractable, e.g.: arbitrary fermion masses and properties.

3) Are based on some sort of global minimisation as the core computation, which isn't a local function. It's solving physics differential equations numerically, sure, but not in the same "local way" that the Universe does.

4) Outputs some simple scalar value or 1D graph as the result. I've only seen a small handful of codes that can output a "picture", as in a rendering of some aspect of a volumetric field.

5) Can't model most aspects of QM and/or SR due to the corner-cutting somewhere.

Probably the best extant codes are the ones used for electromagnetic simulations for radar or radiofrequency systems. Due to the long (macroscopic) wavelengths, these inherently required a QED-style treatment. Similarly, correctly handling things like doppler shifts requires SR.

[yummypaint]

The simplifications facilitated by lattice techniques are one of the main features. The non-perturbative nature of QCD makes it impossible to do many calculations that would be trivial in QED. As two strongly interacting particles are separated, the strength of their interaction increases, which is the opposite of everything else we're used to. In QED, you can often safely consider the first few feynman diagrams to be a good approximation of the whole process. In QCD, infinitely many feynman diagrams contribute non-negligibly to the result, which is why traditional methods fail. Here is an example of lattice methods applied to nuclear properties: https://www.frontiersin.org/articles/10.3389/fphy.2020.00174...

[ShinyRice]

Maybe you should start with understanding non relativistic quantum mechanics before understanding QFT. QFT's only a small jump from QM, more or less. As well as understanding classical field theory and Noether's theorem. There are some ad hoc things done seemingly at random, like having to add terms to a Lagrangian to make it invariant under U(1) transformations, and that may seem weird at first, but it's those leaps of faith that got us to where we are.

[perl4ever]

I agree with a lot of people that Feynman's descriptions of physics are appealing but I tend to feel (although it could be just me) that it's more about making you feel like it's intuitive than really transferring his intuition to you.

It's sort of like you go skydiving for the first time, and you go on a tandem jump where you're strapped to the instructor, and it's an amazing experience, but you didn't really do anything. Or you ride on the back of a motorcycle, etc...

But Feynman's explanations give me the tantalizing feeling that something even better is possible. One general direction I can imagine is that I suspect a truly intuitive understanding would start with more general math describing any quantum theory and avoid specifics at first that relate to real world physics.

Unfortunately, mathematicians are addicted to using named of other mathematicians as shorthand (as you do in your short comment) and I think that's a sign of where things go haywire for a layperson. As long as you're dropping names, you are on the wrong track as far as explaining goes. Feynman had a much quoted comment that's associated in my mind, about how when you just know the name of something, you know nothing about it.