Exploring the Elegance and Complexity of Classical Chromodynamics

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In summary: Is that what you meant when you said 'classical solution'?Yes, malawi_ Glenn, That is exactly what I meant...
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ghery
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Hello:

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.

Regards
 
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  • #2
Are you saying that quark confinement can only be quantum ?
 
  • #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?
 
  • #4
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?
 
  • #5
Yes, malawi_ Glenn, That is exactly what I meant...

Thanks
 
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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!
 
  • #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.
 
  • #9
"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.
 
  • #10
Haelfix said:
It was a real pain and took awhile to calculate. Also pretty ugly and perfectly useless for the real world, but an exercise nonetheless.
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.
 

1. What is Classical Chromodynamics?

Classical Chromodynamics, also known as QCD, is a theory in particle physics that describes the strong nuclear force, which is responsible for binding quarks and gluons together to form particles such as protons and neutrons.

2. How does Classical Chromodynamics explain the behavior of quarks and gluons?

Classical Chromodynamics uses mathematical equations to describe the interactions between quarks and gluons. These equations are based on the principles of quantum field theory and the symmetries of the strong force.

3. What is the role of color charge in Classical Chromodynamics?

Color charge is a property of quarks and gluons that is analogous to electric charge. In Classical Chromodynamics, the strong force is mediated by gluons, which carry color charge and interact with quarks to hold them together.

4. How is Classical Chromodynamics related to other theories in physics?

Classical Chromodynamics is one of the three fundamental forces in the Standard Model of particle physics, along with the electromagnetic and weak forces. It is also closely related to general relativity, which describes the force of gravity.

5. What are the current challenges in understanding Classical Chromodynamics?

One of the main challenges in understanding Classical Chromodynamics is the phenomenon of confinement, which explains why quarks and gluons cannot exist as free particles. Another challenge is to reconcile QCD with the theory of gravity and to develop a unified theory of all four fundamental forces.

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