A gauge field [itex] W_\mu [/itex] is known to transform as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

W_\mu\to W'_\mu=UW_\mu U^{-1} +(\partial_\mu U)U^{-1}

[/tex]

under a gauge transformation [itex]U[/itex], where the first term [itex]UW_\mu U^{-1}[/itex] means it transforms under the adjoint representation. Can anyone explain to me why it means a transformation under the adjoint representation? all I know is the definition of the adjoint representation

[tex] [T_i]_{jk}=-if_{ijk} [/tex]

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# Adjoint transformation of gauge fields

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