Appendix C: The Generators of the SU(2) and SU(3) Groups

Abstract

The three Pauli matrices are:

$\displaystyle \sigma ^1=\left( \begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array} \right) \;\;\;\;\;\;\sigma ^2=\left( \begin{array}{ll} 0 & -i \\ i & 0 \end{array} \right) \;\;\;\;\;\;\sigma ^3=\left( \begin{array}{ll} 1 & 0 \\ 0 & -1 \end{array} \right)~~~~~~{\rm (C.1)}$

$\displaystyle \sigma _i\sigma _j=\delta _{ij}+i\varepsilon _{ijk}\sigma _k~~~~~~{\rm (C.2)}$

The three generators of the $SU\left( 2\right)$ group are $T_a=\frac 12\sigma _a$.