# References for classical Yang-Mills theory

I am looking for a reference to study classical (i.e., not quantized) Yang-Mills theory.

Most of the sources I find focus on mathematical aspects of the theory, like Bleecker's book Gauge theory and variational principles, or Baez & Muniain's Gauge fields, knots and gravity.

But I am more interested something similar to the standard development of electromagnetism, as can be found, for example, in Landau & Lifchitz's course on theoretical physics. To be more exact, I would like to learn about the field equations (Yang-Mills and Einstein equations), but also about the corresponding Lorentz Law, the energy of the Yang-Mills field,... and the analogous concepts of what is made for the electromagnetism.

That is, I look for a rigorous exposition where, at the same time, I could learn whether it is possible to prove, at the classical level, the quick decrease of the strong interaction, and things like that.

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If by the "quick decrease of the strong interaction" you mean asymptotic freedom, you are not going to find a proof of this at the classical level because it is an intrinsically quantum effect. –  Jeff Harvey Jan 10 '12 at 19:00
Mmm.. No, I meant the fact that the strong force is much stronger than electromagnetism or gravitation at the atomic scale, but it becomes negligible at large scale (I guess this is not the same of "asymptotic freedom"). To see this, you would only need a kind of analogous of "Coulomb's law" for the strong force... –  Jose Navarro Jan 11 '12 at 10:11
The strong force is negligible at large distances because the "charge" it couples to is confined. I don't think you are going to understand confinement from classical gauge theory either. –  Jeff Harvey Jan 12 '12 at 6:43

This is underrepresented in the literature. I have Nakahara and have looked at Frenkel (both listed in other answers) as well as many other "standard" references. The best book reference for classical YM theory that I found was Rubakov's Classical Theory of Gauge Fields.

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Thanks, Steve. I didn't know that book, but it seems precisely the kind of reference I'm looking for. And I totally agree this topic is underrepresented in the literature. –  Jose Navarro Jan 11 '12 at 10:03
Full text of Rubakov's book is available here: gen.lib.rus.ec/… –  Dmitri Pavlov Jan 12 '12 at 10:39

Have you tried the book "the Geometry of physics" by Th. Frankel?

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Thanks for the reference, Liviu. I remembered having looked at this book, but I didn't try it seriously. I'll take it again. –  Jose Navarro Jan 11 '12 at 9:57

I would add: Atiyah, Michael F. (1979), Geometry of Yang–Mills fields and then the book of the same author about gauge theories: Atiyah, Michael F. (1988e), Collected works. Vol. 5 Gauge theories

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Thank you, Jon. But I think these references are "too sophisticated" (and too mathematically oriented) for my purposes. –  Jose Navarro Jan 11 '12 at 10:01

Maybe you can have a look to Nakahara's Geometry, Topology and Physics, or is it too elementary for your purposes?

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I didn't knew of this book, but it seems nice. Definitely, another petition for the library of the Department... –  Jose Navarro Jan 11 '12 at 9:59