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I don't really know how you can understand Feynman diagrams without seeing how annihilation and creation operators act on the vacuum. They are the mathematical
by alephu5 7y ago
I don't really know how you can understand Feynman diagrams without seeing how annihilation and creation operators act on the vacuum. They are the mathematical building blocks of qft; formally they are linear operators that represent the creation or annihilation of particles.
If you apply an annihilation operator to a state containing no particles then the string gets deleted from your equation. Moreover if you swap the order of two operators you get an artifact (they're matrices after all), so a•b = b•a + c and so in qft calculations you swap your strings of operators around until you end up distilling it down to just a few non-vanishing artifacts that can be calculated. There's something called wick's theorem that the result of this process can actually be mapped onto a graph if you specify the initial and final state.
- mnl 7y agoYeah, normal ordering and contractions, if we're expanding the fields in terms of such operators when doing canonical quantization using Fock spaces. There's a lot of stuff going on there. The fact that we can draw nice pictures representing the terms of a perturbation theory doesn't mean that you can skip a regular course on QFT to understand what practitioners mean when they use them. Again, not stressing this while showing tree level Feynman diagrams as if they were straight representations of particle interactions may give wrong ideas to the unsuspecting readers.