& 0 \\[-2ex]
    1 & 0 & 0 \\
  \end{array}
\right).\label{eq:A1}\end{gathered}$$ They have the following property: $$\label{eq:A2}
{\rm Sp}\lambda^{a}\lambda^{b}=2\delta_{ab}$$ and satisfy the commutation relations, $$\label{eq:A3}
[\lambda^{a},\lambda^{b}]=2if^{abc}\lambda^{c}.$$ The structure constants $f^{abc}$ of the SU(3) group, according to Eq. (\[eq:A2\]), are found to be $$f^{abc}=-{i\over 4}{\rm Sp}\,\lambda^{c}[\lambda^{a},\lambda^{b}],$$ whence $$\label{eq:A4}
f^{abc}=-f^{bac}=f^{bca}.$$ One can easily find the numerical values of the structure constants, $$\label{eq:A5}
f^{123}=1, \quad f^{147}=-f_{156}=f^{246}=f^{257}=f^{345}=-f^{367}={1\over 2}, \quad f^{456}=f^{678}={\sqrt{3}\over 2}.$$ All other numerical values of $f^{abc}$ not related to the indicated above by permutation are zero. The anticommutator of the Gell-Mann matrices, as well as the commutator, is linear in $\lambda_{a}$: $$\label{eq:A6}
\{\lambda^{a},\lambda^{b}\}={4\over 3}\delta_{ab}+2d^{abc}\lambda^{c}.$$ The coefficients $d^{abc}$, symmetric over all indices, are given by $$d^{abc}={1\over 4}{\rm Sp}\,\lambda^{c}\{\lambda^{a},\lambda^{b}\}.$$ The following their values are different from zero: $$\begin{gathered}
d^{118}=d^{228}=d^{338}=-d^{888}={1\over\sqrt{3}}, \nonumber \\
d^{146}=d^{157}=d^{256}=d^{344}=d^{355}=-d^{247}=-d^{366}=-d^{377}={1\over 2}, \nonumber \\
d^{448}=d^{558}=d^{668}=d^{778}=-{1\over2\sqrt{3}}. \label{eq:A8}\end{gathered}$$

[99]{}

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