There are often complaints that quantum field theory is impossible to understand, e.g. CIP repeatedly wrote about buying more and more books about it, but still having trouble comprehending it.
If people have a problem in or with physics, it often is about math and mostly for two reasons:
i) The math used in physics often seems more complicated than what one learns in high school.
ii) The "physicist math" is often ill defined - the physicists often argue, with some justification, that they are way ahead of mathematicians.
Both problems are prominent in QFT: spinors, gauge theory and all that require a lot of advanced math, but some basic concepts, e.g. path integrals, are not even well defined.
My only recommendation is to keep in mind that math is in the end only about re-arranging empty sets and can always be learned given enough time and the proper text books.
Btw I initially learned QFT from Ryder, but there are gentler introductions, e.g. QFT Demystified.
But I suspect that this is not really the problem of CIP et al.
I believe QFT is so hard to understand, because the (classical) models our brain constructs when we learn something are either unavailable or fail completely. I suspect that most people understand even relativity and quantum mechanics by using such models and learning when to switch between them. There is Schroedinger's wave, there are atoms jumping from one state to another, particles tunneling through barriers etc.
I suspect that the need for such classical models is what drives the interpretation debate from Bohm's guiding wave to the splitting of many worlds.
Unfortunately, with QFT the math is pretty much all there is.
But there is some hope for CIP et al. which requires trying something different: lattice field theory (pdf).
A Wick rotation transforms the path integral(s) of QFT into an exercise in statistical mechanics (this trick is not always available, but it works e.g. for QCD). All of a sudden the math is well defined and simple enough that one can simulate QFT on a computer, even at home on a laptop. Btw I would recommend to begin with simulations of the Ising model and the Potts model before moving on to full QCD 8-)
Of course, one needs to keep in mind that "computer time" is very different from real time and the translation from the lattice back to reality can be tricky. But it helps a lot understanding Wilson renormalization, triviality of the Higgs, QCD confinement and other stuff.
And via Boltzmann machines there is even a bridge to neural networks and AI (pdf).
2 comments:
I don't want to minimize my conceptual confusions about QFT, but I think my basic problem is lack of proficiency. If you told me that my PhD would be withdrawn if I couldn't calculate the Lamb shift from scratch, I'd have to hand it over. I've done some of that kind of calculation, but never attained any skill that I recall. Also, I never really learned any of the higher gauge stuff.
>> Lamb shift
I think Lamb shift ( i.e. qed at 1-loop) is to qed as the H-atom is to quantum mechanics; usually you do the calculation once (as a student when your brain is still young) and it is amazing when you finally calculate a real world result.
And if you learn a bit more more then you really appreciate how awesome it all is: e.g.the qed perturbation series does not converge in the usual sense, the path integral of the H-atom is quite tricky, due to the action being unbounded from below ( because of the 1/r term from the potential) etc.
But I think it is ok to forget some of the details, which you can look up and remember again if needed. I would think that I basically understand how a computer works, even if I don't know how the registers, etc. are arranged in an intel microprocessor.
>> the higher gauge stuff
Lattice field theory helps with that a bit, because gauge fields become matrices associated with the links, etc. and one can get a feeling for non-abelian gauge fields from that imho.
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