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.
Right... I knew this.. ''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!'' > ''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.'' Yes, but it CANNOT BE A coincidence without resorting to the Antropic Principle... Hawking, well-more intelligent than both of us together even admits this/. This is why electrons and protons HAD to be produced in EQUAL PROPORTIONS... not only that, but there has to be an attractive and negative force in the QCD model to allow this. ''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.'' This is why we SHOULD RESORT to using a mediator, such as an atom. ''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!'' Yes... i agree.
No? I don't follow this at all... There is a photon, there is an electron. We don't need atoms to have electromagentic forces.
Now... why should we ''SHOULD RESORT to using a mediator, such as an atom.'' (myself here) Because when two photons are able to hit off each other, they will release enough energy within the vacuum to create a positron eletron pair. According to theory, the positron will be forced to leave the atom, instead of forcing itself back into it's partner, because the proton has a positive energy.
Actually, if what you mean that the atom is a shell, then how is the shell created...? Think....? Think hard about it please.
Slipped on his own shoelace, as usual, Ben now.../ James... why did you put this here? Was my work too vulgure?
Reiku--- Try to keep up. I don't care about atoms. I only care about protons, neutrons, and electrons. At some point in the history of the universe, when the kinetic energy of all particles was large enough (say within the first minute) there were ONLY protons, neutrons, and electrons. There were no atoms. This is not true in general. It takes 1022 keV of energy to produce an electron/positron pair from photon, photon scattering. If we were to do the photon-photon scattering experiment at energies LESS than 1022 keV, then nothing would happen. Reiku---everybody doesn't have hours to while away at the computer. Please keep the discussion on topic, as this is an alpha thread. If you need to refresh yourself on the rules, please do so.
Hmm. Reiku was the only one interested here, and he is no longer with us. Unless there is a request, I think I will end this thread. Once QuarkHead finished his discussion on manifolds, I will try to insert whatever I know about the physical applications (I promise, it's not much), and will do a big thread on Lie Algebras as they apply to physics.
That would be great! I am dying to know what these bold numbers (like 3) mean. About technicolor, what kind of group does it use, instead of SU(3)?
The Technicolor group is usually SU(3) or SU(2) or something like that. I will try to make a more or less complete introduction to Lie Algebras and physics, although I fear it would be too long. But I'll see what I can do.
Well, QCD is an effective theory. So the symmetry between the techni-fermions has nothing to do with the symmetry between the quarks. It's just like the isospin example that I used---below a certain energy, isospin is a good symmetry. But when you start to probe the finer details, the symmetry kind of dissolves---it's like a painting. If you stand far enough away, you see a flower, but if you look closely, you see a bunch of brush strokes, and you can't see a flower anymore.
Yeah, I've been slacking on that, sorry. Like all here (I hope) I shall be hors de combat for a while, but maybe next week (shit - that's next year!) I will knuckle down to it (assuming I haven't killed off my last few brain cells!). Actually, one probably could at least introduce Lie groups simply as arbitrary matrix groups, though I doubt their significance would be easy to see in that approach. And I seriously doubt their algebras would make any sense at all until tangent spaces on manifolds are defined.
This is the canonical approach in physicsPlease Register or Log in to view the hidden image! This is what we really use them for, anyway, and any discussion I give about physics will be along these lines (sorry to disappoint).
I can't believe you just said that! I can just about imagine a real mathematician going all gooey over a definition like, say, the set of all invertible, symmetric matrices with det =1 is a Lie group. As I am not a real mathematician, I cannot say. It certainly doesn't do it for me, though I am, of course familiar with these sorts of definitions, and their derivations. But I would assume (not being any sort of physicist), you guys might prefer to pin it to some "real world" scenario, whatever that means? Anyway, enough. I am about to go get hammered, it being Xmas eve. I wish you all a good Xmas, and a more peaceful world (hah!) next year. Truly I do.....
