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Structure of the atom - strong interaction and colour charge.

  1. Jan 17, 2009 #1
    I am having some difficulty understanding the concept of colour charge.
    I realise that protons and neutrons are made up of a different number of quarks, and this is how they have the charges +1 and zero.

    I then realised that different quarks have color charge and that in a hadron (protons and neutrons included), the total colour charge would be zero. I have read that gluons also have some sort of colour charge and mediate a strong force, which keeps the quarks together.

    Quite simple I am confused about the following:

    • Why in hadrons the total colour charge is zero?
    • The colour charges of the different quarks present in the proton?
    • The colour charges of the different quarks present in the neutron?
    • How gluons affect the colour charge?

    ....and finally how all of this affects the residual strong force (keeping the protons and neutrons together)??

    Thanks in advance.
    Adam
     
  2. jcsd
  3. Jan 17, 2009 #2

    malawi_glenn

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    well why they (hadrons) must have total color charge is not understood yet on theoretical level as far as I know it..
    The math society Clay Mathematics Institute has a 1 milion dollar reward for an exact solution to colour con nement in 4 dimensions (3 space, 1time); http://www.claymath.org/millennium/Yang-Mills Theory/yangmills.pdf

    The color charges of the quarks are constantly changing due the glouns, the gluons take away a colour of a quark and gives it new one. i.e a blue quark interact with a red-antiblue gluon -> the quark turns to red.

    How one builds up the strong force between hadrons from QCD, there are many approaches. Lattice QCD and Chiral Perturbation Theory (ChPT) are the most common ones I think. In Lattice QCD one discretize the space-time and in ChPT one uses the symmetries of the QCD lagrangian to construct an effective quantum field theory where the lighest mesons (meson octuplet) and baryons are massless Nambu-Goldstone bososn. But then one has spontaneous symmetry breaking since meson octuplet only exists for pesudoscalars. Finally one has explicit symmetry breaking due to non-zero (quark and) meson masses.
     
  4. Jan 17, 2009 #3
    They are made up of different quarks, different flavors, but to a rather very good accuracy, their structures in terms of quarks and gluons is the same provided you interchange up and down.

    If I understand the Clay mathematical institute prize description, the problem is about mass-gap, not confinement. Although it's true they are probably related, in Gribov's theory of quark confinement glueballs would not exist at all, so the mass-gap problem would be ill-posed if Gribov's vision is correct (for instance).
     
  5. Jan 17, 2009 #4
    The simplest way to describe it is in terms of symmetry. The color symmetry SU(3) is exact, which means that there must be no way of telling if and when the three colors are all changed ("transformed") in a consistent way. This answers your first question -- if hadrons had an observable color, it would change during such a transformation, "breaking" the exact symmetry.

    So not only are the colors of the quarks in a proton or neutron constantly changing, as malawi_glenn correctly notes, they can't individually be well defined in the first place. Whatever you chose to call the color of a particular quark in a nucleon, you could immediately transform it to a different color with no observable effects.

    I got distracted by the Clay Institute's official problem description while writing the above, which let me see that on page three they include three parts to the problem, namely the mass gap, confinement, and chiral symmetry breaking.
     
  6. Jan 17, 2009 #5
    Page 3 describes properties for QCD to be a valid description of hadrons. It is not a description of the problem. The problem is stated page 6.
     
  7. Jan 17, 2009 #6
    Ah, I see. Should have kept reading. They demote confinement to just one of "many natural extensions of the Millenium problem".
     
  8. Jan 18, 2009 #7

    malawi_glenn

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    I should have better memory, I should have read the yang mills millenium problem again before i posted :-)

    Great humanino! The true master of QCD of this forum I would say!
     
  9. Jan 21, 2009 #8
    This has really helped me in understanding. Can someone now explain to me how the residual strong force works with quarks in the hadrons to prevent protons from repelling each other?

    Some maths is ok...but don't overwhelm me (I'm just 15)

    Thanks in advance
    Adam

    ps - this stuff is truly amazing!
     
  10. Jan 22, 2009 #9

    malawi_glenn

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    That question is on nobel prize physics level...
     
  11. Jan 22, 2009 #10
    One could try discussing it in terms of pion exchange, that could be about the right level, though I'm not volunteering.
     
  12. Jan 22, 2009 #11

    malawi_glenn

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    The good ol pion-, rho- and omega exchange potentials right, which provides a quantitive feeling of the general feuatures of the nucleon-nucleon force. But what is nices is the Chiral Perturbation Theory, since it uses the symmetries of QCD and is in that way an effective QCD theory.
     
  13. Jan 22, 2009 #12
    Please go ahead, and introduce to me Chiral Perturbation Theory
     
  14. Jan 22, 2009 #13

    malawi_glenn

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    you first need to know lagrangians, chiral symmetry etc, graduate physics this is..
     
  15. Jan 22, 2009 #14
    Oh...I wish I could do this right now. High school physics isn't this interesting.
    Are there any alternatives?
    The meson transfer theory?
     
  16. Jan 22, 2009 #15

    malawi_glenn

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    yeah, one needs to know pretty much quantum field theory etc to do modern subatomic physics, one must starts from the basics hehe.

    Well the pion exchange stuff was done in the 60's and is not as advanced as ChPT but still, gradudate level physics.
     
  17. Jan 22, 2009 #16
    I see.
    I am in the process of learning all the basics while still interested in the higher level physics.

    At the moment I am learning calculus - something vital for the study of classical mechanics which in turn is needed for the study of quantum mechanics.
     
  18. Jan 22, 2009 #17

    malawi_glenn

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    Yes, we must all learn how to crawl before we can walk, and walk before we can run.

    Calculus is important, but never underestimate algebra - linear algebra and abstract algebra. Differential geometry and complex analysis are also important in modern physics. Other physics courses which one must master (besides quantum mechanics) is electromagnetism, analytical mechanics and special relativity.

    Learn slow, and make sure you learn the basics very well, it will pay off in the long run.
     
  19. Jan 24, 2009 #18
    Something in me feels like if I can't explain something to someone intelligent but not versed in the jargon of the trade, then I haven't really understood it. So a challenge for all: explain hadron interaction, as detailed as possible, but without mentioning anything that a high school student doesn't know.

    Doesn't actually need to include that much: some plausible reason for confinement (Wilson's area law, gauge theory <-> string <-> rubber bands), enough about colour to explain why mesons and hadrons are the low energy spectra, and enough of interactions to relate the mass of pions to the range of hadron interactions. Extra bonus: pion mass generation (though my instinct is that it would take too long, though not necessarily impossible).
     
  20. Jan 24, 2009 #19
    I could probably do the first couple...but i'm afraid i wouldn't be as specific as you like, not very gud at explaining this stuff

    However if you really want to nail the basics and get some good stuff aswell I would check out these lectures, he really explains the basics well aswell and talks about some more advanced stuff.

    http://uk.youtube.com/watch?v=rsnEUApVHgI&feature=SeriesPlayList&p=095393D5B42B2266&index=16

    http://uk.youtube.com/watch?v=fbiQ61NScU0&feature=SeriesPlayList&p=095393D5B42B2266&index=17

    http://uk.youtube.com/watch?v=0RrWEBDMo80&feature=SeriesPlayList&p=095393D5B42B2266&index=18

    http://uk.youtube.com/watch?v=yzP6TdBAIcU&feature=SeriesPlayList&p=095393D5B42B2266&index=19

    They're pretty long though (but interesting enough to keep you hooked!) Also if you like these ones i'd seriously recommend his one on nukes (the best one imo)
     
  21. Jan 24, 2009 #20
    Spot on :)
    That is exactly what I want. I'm really interested in physics and want the basics, since I'm still learning all the math I need. Dreaming of the day when I can start using complex equations, and use numbers to explain concepts.

    :P
     
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