I think one of the more underrated pieces of software out right now is Maple. It's a solid piece of software and is fantastic at differential equations (which are indispensable everywhere). Not only that, but it can solve them numerically and symbolically. Also it has a package for nearly...
The whole vibration concept is more of a way to visualize and mathematically model QFT, since it is so hard to imagine things that are that small at that amount of energy. The "photons as an excitement of another field" is mostly just for describing virtual particles.
Virtual particles are...
Well no. Even if you're going smaller than a quark, you're just looking at an even smaller quanta of matter. Even then, there probably isn't anything smaller than a lepton or boson.
Right now I've been listening to a lot of Swans and stuff. Their newer, more experimental material is probably some of the best music to come out this decade.
Before I begin, I would like to say what I am about to ask would require some sort of top-top-bottom bound state for it to function. Which (to my knowledge) has not been experimentally or theoretically predicted. Also, in case if you are wondering- no, this is not a homework question.
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So...
I don't have a PhD, so take what I say with a grain of salt. But, from what I understand, renormalization is when a loop or something similar arises in a diagram and you need to take out any possible infinities; because any infinity in an actual calculation would make the diagram, and...
I would suggest buying Introduction to Elementary Particles by Griffiths. It may not give instructions on how to create diagrams, but it gives excellent instructions on how to find amplitudes, decays, and cross sections, given a diagram.
Well, not to my knowledge. Chances are you'll have thins like textbooks, google, paper archives and databases, etc., to do the memorization for you. All you really have to do is understand what you're learning. Even if that subject is hardly understood.