What Makes Classical Chromodynamics Unique in Understanding Strong Interactions?

[ghery]

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

 

[humanino]

Are you saying that quark confinement can only be quantum ?

 

[ghery]

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?

 

[malawi_glenn]

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?

 

[ghery]

Yes, malawi_ Glenn, That is exactly what I meant...

Thanks

 

[malawi_glenn]

Yes, malawi_ Glenn, That is exactly what I meant...

Thanks

Don't know if Iam allowed to link to this, since it is not a published article, but it is the only thing I found about 'classical' QCD:

http://arxiv.org/PS_cache/hep-th/pdf/0607/0607203v2.pdf

 

[Sheets]

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!

 

[humanino]

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.

 

[Haelfix]

"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.

 

[humanino]

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.