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How do we get the potentials of the 3-fundamental forces from first principles? Quantum Field Theory (1) Specifically, we take the Fourier Transform of the Feynman diagram that describes each force We can *almost* get all 3 this way. Everything except the Strong Force (2/N)pic.twitter.com/5ajfg9baf4
For the Gluons, we *do* obtain the "Coulomb" term (1/r) but we don't get the linear term (kr). To find out what’s going on, we’ll need a couple facts.pic.twitter.com/oJ1M69TCI4
Charge, mass etc *change* depending on the energy scale!
•The Strong Force has the unique property that α 
as E
•There is an E where out denominator will become 0 and hence our series will diverge!
This is called a "Landau Pole" and is exactly the source of our troublespic.twitter.com/FL9VnoL312
QCD becomes ill defined at: E≲100 GeV ⇔ distance ≳10⁻¹⁵m (found by solving previous eqn) So it's no surprise that the (kr) term isn't predicted by QCD, since we never even had a well-defined theory at the distance scales which this term would be relevant from the very startpic.twitter.com/l3GDG9oM2v
Since our perturbation theory breaks down, we say that the k*r term is generated "non-perturbatively", which basically means ¯\_(ツ)_/¯ Precisely why and how this all happens is known as the problem of Color Confinement, and remains an unsolved problem to this day.
However, we are still able to write down a perfectly well defined Quantum Field Theory the moment QCD breaks down. The new theory however is in terms of neutrons, protons, pions etc. and not of 'fundamental' quarks. That discussion will have to wait for another day.
KING SHIT
Wait... if successive terms of your perturbation series don’t get smaller... it’s a bad series and your results won’t make sense?! Attn 75% or condensed matter theory papers out there
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