(1) The Weak Force is extremely short ranged: its potential is *almost* Coulomb's Law (2), but exponentially suppressed due to the fact its force carriers W⁺⁻, Z⁰ are massive (i.e. m≠ 0)
(3) The second term in the last equation (kr) is what makes the strong force so "strong"
(3) The second term in the last equation (kr) is what makes the strong force so "strong"
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)
(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)
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.
To find out what’s going on, we’ll need a couple facts.
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 troubles
•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 troubles
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 start
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 start
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.
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.
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.
thank you for coming to my TED Talk
