Thursday, March 31, 2016

quantum chromodynamics - Mathematically, what is color charge?


A similar question was asked here, but the answer didn't address the following, at least not in a way that I could understand.


Electric charge is simple - it's just a real scalar quantity. Ignoring units and possible quantization, you could write $q \in \mathbb{R}$. Combination of electric charges is just arithmetic addition: $ q_{net} = q_1 + q_2 $.


Now to color charge. Because there are three "components", I am tempted to conclude that color charges are members of $\mathbb{R}^3$. However, I've read that "red plus green plus blue equals colorless", which seems to rule out this idea. I can only think that either:




  • red, green and blue are not orthogonal, or

  • "colorless" doesn't mean zero color charge (unlikely), or

  • color charges don't combine in a simple way like vector addition


In formulating an answer, please consider that I know some mathematics (vectors, matrices, complex numbers, calculus) but almost nothing about symmetry groups or Lie algebras.




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