Gell-Mann matrices

The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3x3 traceless Hermitian matrices utilized in the study of the strong interaction in particle physics. They span the Lie algebra of the SU(3) group in the defining representation.

and ${\displaystyle g_{i}=\lambda _{i}/2}$.

These matrices are traceless, Hermitian (so they can generate unitary matrix group elements through exponentiation), and obey the extra trace orthonormality relation. These properties were chosen by Gell-Mann because they then naturally generalize the Pauli matrices for SU(2) to SU(3), which formed the basis for Gell-Mann's quark model. Gell-Mann's generalization further extends to general SU(n). For their connection to the standard basis of Lie algebras, see the Weyl-Cartan basis.

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