Appendix D. Color Charges of Quarks and Gluons

Abstract

In $SU\left( 2\right)$, the charge operator is:

$\displaystyle Q=eT_3=\frac 12\left( \begin{array}{cc} e & 0 \\ 0 & -e \end{array} \right) ~~~~~~~{\rm (D.1)}$

The quarks form a doublet in the fundamental representation of $SU\left( 2\right)$:

$\displaystyle q=\left( \begin{array}{c} q_R \\ q_B \end{array} \right) \;\;\;\;\;\;Q\left( \begin{array}{c} q_R \\ q_B \end{array} \right) =\frac 12e\left( \begin{array}{c} q_R \\ -q_B \end{array} \right)~~~~~~~{\rm (D.2)}$

The red and blue quarks have respectively color charges $\frac 12e$ and $-\frac 12e$.