Gell-Mann Matrix

The eight Gell-Mann matrices , , are an example of the set of generators of the Lie algebra associated to the special unitary group . Explicitly, these matrices have the form

			(1)
			(2)
			(3)
			(4)
			(5)
			(6)
			(7)
			(8)

Note that the eight Gell-Mann matrices are traceless and Hermitian and satisfy the relation where denotes the Kronecker delta. Moreover, in the notation above, is symmetric for , antisymmetric for , and diagonal for . Because of these properties, one can view the Gell-Mann matrices as a three-dimensional generalization of the Pauli matrices, which (with slight modification) generate the Lie algebra associated to .

These matrices are particularly important in both mathematics and physics. For example, these matrices (and their generalizations) are important in Lie theory. In addition, they also play an important role in physics where they can be thought to model the eight gluons that mediate the strong force quantum chromodynamics, an analogue of the Pauli matrices well-adapted to applications in the realm of quantum mechanics.