BenTheMan
12-20-07, 12:52 AM
This is in response to a question posed by Reiku in another thread.
I should warn you, I am going hunting and will be sans internet untill at least the 23rd. So the questions may stack up. Apologies!
First QCD.
QCD (Quantum Chromodynamics) is the theory of the strong interaction, which binds the nucleons together. QCD describes quarks and anti-quarks of three colors. What does color mean? Well, color is just another word for charge. In electomagnetism, there is one charge, called negative, and its anti-charge, called positive. In QCD, there are three charges, called red, green, and blue, and their anti-charges, called anti-red, anti-green, and anti-blue.
In electromagnetism, the electrons interract by exchanging virtual photons. Because there is only one charge, there is only one type of photon. Further, because there is only one type of photon, the photon cannot interract with itself.
In QCD, the situation is much more complicated. There are three charges, which means there are eight different types of force carriers, called gluons. The gluons can interract with themselves, which can make things difficult to calculate.
Technical aside: EM is based on a U(1) gauge theory. U(1) is the simplest lie group, and has dimension 1. This is intimately related to the fact that there is only one photon. U(1) also has a fundamental representation of dimension 1, and THIS is intimately related to the fact that there is only one type of charge! (If you are reading this, then you are saying...Yeah, that's the ONLY representation of U(1).) The same goes for QCD, which is a gauge theory based on the group SU(3)---the three charges are exactly the fundamental rep of SU(3) (the 3), and the eight gluons are exactly the adjoint representation!
Ok, now a bit of history.
If you were doing phsics in 1920, then you knew about protons, neutrons, and electrons. Well, Pauli had the bright idea to say ``What if protons and neutrons are different faces of the same thing?'' In essence, what he realized is that p and n are pretty similar---they have about the same mass, they are both found in the same place (the neucleus)...it stands to reason that there may be some way to relate the two things.
What he discovered was the isospin symmetry. And it worked great, if you neglect the fact that there is a tiny mass differnece between the proton and neutron.
Well, it worked great untill we started doing higher and higher energy experiments. If we start throwing electrons at the proton, for example, it looks pretty much like a fundamental particle, below an energy of about 1 GeV. But as we start to hit the proton with electrons of about 1 GeV, we start to see some structure emerge---in other words, the experimenters found that the proton and neutron HAD to be treated as composite objects in order to match the data. In fact, this is the type of stuff that Feynman cut his teeth on.
So here's what we have: we thought the protons and neutrons were fundamental, because we had no reason to suspect otherwise. BUT, we started doing experiments that told us that there was no way in HELL that this could be true. Taking p and n as fundamental is perfectly good if you're not shooting too high energy electrons at them, and in many areas of physics, we still consider p and n to be fundamental.
But at high enough energies, the effects that we are ignoring begin to become bigger and bigger, and we can no longer neglect them in our analysis.
This is the idea behind technicolor. We have been treating the quarks as fundamental particles, but what if they aren't? What if QCD is just an effective description, like Pauli's isospin? The question is, what kind of consequences does this theory have?
I will let this topic steep for a few days while I go kill some things, and then I'll get back to you.
I should warn you, I am going hunting and will be sans internet untill at least the 23rd. So the questions may stack up. Apologies!
First QCD.
QCD (Quantum Chromodynamics) is the theory of the strong interaction, which binds the nucleons together. QCD describes quarks and anti-quarks of three colors. What does color mean? Well, color is just another word for charge. In electomagnetism, there is one charge, called negative, and its anti-charge, called positive. In QCD, there are three charges, called red, green, and blue, and their anti-charges, called anti-red, anti-green, and anti-blue.
In electromagnetism, the electrons interract by exchanging virtual photons. Because there is only one charge, there is only one type of photon. Further, because there is only one type of photon, the photon cannot interract with itself.
In QCD, the situation is much more complicated. There are three charges, which means there are eight different types of force carriers, called gluons. The gluons can interract with themselves, which can make things difficult to calculate.
Technical aside: EM is based on a U(1) gauge theory. U(1) is the simplest lie group, and has dimension 1. This is intimately related to the fact that there is only one photon. U(1) also has a fundamental representation of dimension 1, and THIS is intimately related to the fact that there is only one type of charge! (If you are reading this, then you are saying...Yeah, that's the ONLY representation of U(1).) The same goes for QCD, which is a gauge theory based on the group SU(3)---the three charges are exactly the fundamental rep of SU(3) (the 3), and the eight gluons are exactly the adjoint representation!
Ok, now a bit of history.
If you were doing phsics in 1920, then you knew about protons, neutrons, and electrons. Well, Pauli had the bright idea to say ``What if protons and neutrons are different faces of the same thing?'' In essence, what he realized is that p and n are pretty similar---they have about the same mass, they are both found in the same place (the neucleus)...it stands to reason that there may be some way to relate the two things.
What he discovered was the isospin symmetry. And it worked great, if you neglect the fact that there is a tiny mass differnece between the proton and neutron.
Well, it worked great untill we started doing higher and higher energy experiments. If we start throwing electrons at the proton, for example, it looks pretty much like a fundamental particle, below an energy of about 1 GeV. But as we start to hit the proton with electrons of about 1 GeV, we start to see some structure emerge---in other words, the experimenters found that the proton and neutron HAD to be treated as composite objects in order to match the data. In fact, this is the type of stuff that Feynman cut his teeth on.
So here's what we have: we thought the protons and neutrons were fundamental, because we had no reason to suspect otherwise. BUT, we started doing experiments that told us that there was no way in HELL that this could be true. Taking p and n as fundamental is perfectly good if you're not shooting too high energy electrons at them, and in many areas of physics, we still consider p and n to be fundamental.
But at high enough energies, the effects that we are ignoring begin to become bigger and bigger, and we can no longer neglect them in our analysis.
This is the idea behind technicolor. We have been treating the quarks as fundamental particles, but what if they aren't? What if QCD is just an effective description, like Pauli's isospin? The question is, what kind of consequences does this theory have?
I will let this topic steep for a few days while I go kill some things, and then I'll get back to you.