I've been playing around with the QCD Lagrangian to get a better understanding of how it works. I can derive some classical, Maxwell-like equations; the inhomogenous ones are(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\nabla \cdot \vec E^a = -gf^{a}_{bc} \vec A^b \cdot \vec E^c + \rho^a[/tex]

[tex]\nabla \times \vec B^a - \frac{\partial}{\partial t} \vec E^a = \vec J^a + gf^a_{bc} (\Phi^b \vec E^c - \vec A^b \times \vec B^c)[/tex]

The problem is that I'm not quite sure how to interpret these equations. The (gluon) color indices {a, b, c} run from 1 to 8. But there are three kinds of color charge. So how do I interpret the sources [itex]\rho^a[/itex] and [itex]\vec J^a[/itex]?

One thing I attempted was to multiply both equations by the generators [itex]T^a_{ij}[/itex]. This eliminates the gluon color indices {a, b, c} in favor of the quark color indices ij (which then run from 1 to 3). But now there are two indices on everything! One for a color and one for an anti-color. Again, I can't quite figure out how to interpret what it means.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Color currents in classical QCD

**Physics Forums | Science Articles, Homework Help, Discussion**