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Classical Chromodynamics

  1. Aug 26, 2008 #1

    I've heard that quantum chromodynamics describes the strong interaction between quarks, but What is classical chromodynamics? as long as I know qurks are not found free in nature.

  2. jcsd
  3. Aug 26, 2008 #2
    Are you saying that quark confinement can only be quantum ?
  4. Aug 27, 2008 #3
    I am not saying that confinement can only be quantum. What I mean when I said that quarks are not found free in nature, is that is not possible to observe for example two quarks interacting macroscopically..or can they?
  5. Aug 27, 2008 #4


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    You mean, since we have 'classical electrodymanics' description of radiation and matter, and also 'Quantum Electrodynamics' - quantum description of radiation and matter -> where is the classical description of quark-gluon interaction?
  6. Aug 27, 2008 #5
    Yes, malawi_ Glenn, That is exactly what I meant...

  7. Aug 27, 2008 #6


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  8. Aug 27, 2008 #7
    It's a fun little exercise to derive the chromodynamic "Maxwell Equations" from the QCD lagrangian. T.D. Lee's book might do this prior to the section where he develops Hamiltonian QCD, If I remember correctly. Staring at the classical chromodynamics equations of motion make you appreciate the linearity of E+M!
  9. Aug 27, 2008 #8
    The best textbook I know about that, at the level of introduction, is :

    The Geometry of Physics
    An Introduction
    Theodore Frankel
    CUP (1997, 2004)

    Of course this is not the only one. Classical solution to pure glue QCD in Minkowski space have a lot of solutions, but no solitons. Most of those solutions are chaotic. A more advanced reference discussing those aspects is
    Chaos and gauge field theory
    T.S. Biro, S.G. Matinian and B Muller
    World Scientific, Singapore (1994)

    Finally, pure glue QCD solutions in euclidean space are instantons and you probably already know how important they are, and how much has been written about them.
  10. Aug 28, 2008 #9


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    "It's a fun little exercise to derive the chromodynamic "Maxwell Equations" from the QCD lagrangian."

    This was actually part of my competency exam when I was a graduate student. It was a real pain and took awhile to calculate. Also pretty ugly and perfectly useless for the real world, but an exercise nonetheless.
  11. Aug 28, 2008 #10
    You made an exercise proving you are able to calculate. You also know that Maxwell's own original calculations were mostly ugly. The fact that we don't know how to handle those non-linear Yang-Mills equations correctly might reflect the fact that we don't yet fully understand the physics going on. We already know that Yang-Mills theory are most elegantly written on geometrical fiber bundles in terms of forms.
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