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I am trying to generate the Pauli matrices and am using the following formula taken from http://en.wikipedia.org/wiki/SU(3 [Broken])

"In the adjoint representation the generators are represented by (n^2-1)×(n^2-1) matrices whose elements are defined by the structure constants"

[tex](T_a)_{jk} = -if_{ajk}[/tex]

ok - I'm fine up to here. Now it says, "For SU(2), the generators T, in the defining representation, are proportional to the Pauli matrices, via:"

[tex]T_a=\frac{\sigma_a}{2}[/tex]

So here is my problem. I am assuming that j and k run from 1:2. This way T_a is a 2x2 matrix. But lets try this for the first Pauli matrix:

[tex](T_1)_{11} = -if_{111}=0[/tex]

[tex](T_1)_{12} = -if_{112}=0[/tex]

[tex](T_1)_{21} = -if_{121}=0[/tex]

[tex](T_1)_{22} = -if_{122}=0[/tex]

[tex]

\sigma_{1} = \left(\begin{array}{cc}0 & 0\\0 & 0\end{array}\right)[/tex]

Clearly I am doing something wrong...but what?????

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# Pauli Matrices and Structure Constants

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